Question:

There are groups of believers that seem to be attempting to summon, call, or direct the Holy Spirit of God to move among them & do certain things.  Two examples being "Drunk in the Spirit" or "Slain in the Spirit"  Does a believer or a group of believers have the authority or the ability to cause the Spirit of God to manifest Himself in some expected way?

Answer:  

The Holy Spirit is the One Who should be leading.  To the extent that a human being leads, the Holy Spirit lifts off of the people.  When people try to lead God, this is rebellion.  Rebellion is as the sin of witchcraft.  When people try to control the situation or cannot adjust their plans to the mood and will of the Holy Spirit, this hurts the moving of the Holy Spirit.  

The Holy Spirit is orderly.  The Holy Spirit will never lead into disorder.  The Holy Spirit will not lead any person to be disruptive, be out of order, do things that don't edify, or do things that are disrespectful.  

The Holy Spirit moves in many ways.  Sometimes, when He moves, Christians look at the outward appearance and think, "I can do that."   From what I have seen, those who are "drunk in the Spirit" or "slain in the Spirit" are almost always emulating something that the Holy Spirit did once or that they heard that the Holy Spirit did.  It is difficult to make a blanket statement on this.  The counterfeits do not make the real any less real.  Let me just tell you about some things that I have seen.  
 
There was a young man that came to a Church camp meeting as a guest.  He was a big handsome Marine about twenty or so years old.  The other young people looked up to him because he had a great physique.  Anyone observing could see that this was going to his head.  He was not saved.  He thought the whole camp was a joke.  Then there was a meeting where the Spirit moved on many of the young people, and they started going to the front to be prayed for.  This young man got up.  He was looking around with a smirk.  He was very flippant and started to go up to the front just because everyone else was going.  It was obvious that he thought the whole thing was funny.  He started walking from the back to the front.  As he walked down the aisle, something happened.  The Holy Spirit came upon him.  He really didn't know what was happening.  He started to cry.  His knees slowly gave out and he couldn't make it to the front.  The Holy Spirit didn't do this type of thing among these people.  This young man gave his heart to the Lord that night.  
 
There are many well-known celebrities who are known for the way they can touch people and those people fall down.  Some of these are obviously the ones who are getting the glory.  Even when they say glory to God, it seems that every eye is on them.  There is a lot of flash and showmanship.  
 
There was a pastor in a small Church--and independent Church.  Shortly after the pastor had started in his job, a man came to church and asked for prayer for healing.  The pastor called him to the front and prayed for him, laying his hands on the sick man.  The sick man passed out and fell down.  When he woke up, he was healed.  Then, everyone started doing this and falling down.  No one was healed.  The pastor sensed that the Holy Spirit was grieved and told the people to stop.  
 
There was a pastor of a small Church who would allow men to come an preach in his Church.  There are many people running around claiming to have authority, and many of them came.  The pastor was constantly blown around by winds of doctrine.  The pastor rejected orderly worship and headship at a certain point.  He started having slain in the Spirit meetings.  One of the people in his Church was very fat.  The people would sit on chairs and this pastor would lay hands on them so they would be slain.  The poor fat man would really have to work at throwing himself on the floor.  It was silly to see it.  

Question:

What would be the effects on a believer being continually filled with the Holy Spirit during church services? Would the Spirit move a person to a place of complete abandonment as some groups seem to demonstrate?  

Answer:

We have to address the fact that a lot of what is called "being filled with the Spirit" in the church services is actually something other than truly being filled with the Spirit.  It is sometimes hard to know by which spirit a thing is done.  That is why the gift of discernment of spirits is given to the church.  Only a small remnant of the Church has received this gift, however.  

Emotion is not the Holy Spirit. 

Some Christians used to try to get the Holy Spirit to move by singing a song faster and faster because it would cause excitement, but they stopped doing that when they found out that it was just the flesh and not the Holy Spirit. 

Some Christians have used tactics to create emotion with music.  Music can cause a feeling that is emotion, not the Holy Spirit.  There is music that uses an off-beat rhythm that causes a kind of confused emotion.  Some have called this off-beat "rock" or "rock and roll."  There are Christians who think that this off-beat is the Holy Spirit or that the emotion it induces is the Holy Spirit.  Sometimes, anger is projected in the music.  Some of the music is sensual.  Some music projects fear.  Some is demonic.  Some gives glory to a Christian or group of Christians.  All these types of music cause strong emotions.  And all of these types of music are used in Church Services.  These types of music cause the Spirit to lift from the assembly and a different spirit takes the glory.  
 
But the Church can really experience the flow of the anointing.  And it can be in the service or when we are alone or when we meet with only one or two others.  The Holy Spirit can be there. 

We were designed and created to be continually filled with the Holy Spirit.  When you are filled with the Holy Spirit, a peace fills you.  Your mind is activated.  You can hear God's voice more clearly.  You become more loving of everyone around you.  You forgive all who have ever wronged you.  All fear disappears.  You submit to your brothers and sisters in Christ.  You walk in an orderly way.  If the flesh comes in, the Holy Spirit uses some way to let you know that it was just the flesh and that you should not go that way.  
 
Would the Spirit move a person to a place of complete abandonment as some groups seem to demonstrate?

When the Holy Spirit is upon you, He will lead you to abandon all sin.  The Holy Spirit will lead you to abandon insanity and wild, uncontrolled emotion, and will lead you into a sound mind.  He will lead you to abandon all foolishness.  He will lead you to abandon all rebellion.  He will lead you to abandon every order that is not in Scripture (we see many orders in many churches that are not in Scripture).  He will lead you to abandon church services that don't look just like 1 Corinthians 14.  (Realize that services that do not follow this pattern are out of the pattern that God has established.)   
 
There is another kind of abandonment: that is when people get beside themselves with emotion and lose control.  That kind of abandonment causes chaos, not order.  The Holy Spirit will not lead you into this kind of abandonment.  Some Church services go insane, and the Holy Spirit does not lead in that way.  He may lead in ways that we don't understand, but it will always be decent and in order.  The order will rarely follow the types of forms that you see in the stiff and formal churches of the day, but they will follow the orders of the Scripture.  
 
When we turn over control to the Holy Spirit, we cease to follow two things: our own emotion and our own intellect.  The human mind was never created to function without the Holy Anointing upon it.  We need the Holy Spirit for our minds to work correctly.  But the Holy Spirit is not human emotion.  Our human emotions often will be affected by the Holy Spirit, but the Holy Spirit is the God who moved upon the deep at the creation.  He is the third person of the God-head, not a feeling.

We know a lot about the Holy Spirit.  The Holy Spirit is loving.  The Holy Spirit is peaceful.  All the things that the Bible says of love are true of the Holy Spirit.  

We have to look at all the things that God is doing and what the entire Bible says about God's purpose and plan.  We need to understand why God gave the Holy Spirit.  The Holy Spirit is given to lead us into righteousness, holiness, and redemptions.  Read about that here.