Do churches decide where preachers should teach?

Answer:

"For there is no distinction between Jew and Greek; for the same Lord is Lord of all, abounding in riches for all who call on Him; for "Whoever will call on the name of the Lord will be saved." How then will they call on Him in whom they have not believed? How will they believe in Him whom they have not heard? And how will they hear without a preacher? How will they preach unless they are sent? Just as it is written, "How beautiful are the feet of those who bring good news of good things!" However, they did not all heed the good news; for Isaiah says, "Lord, who has believed our report?" So faith comes from hearing, and hearing by the word of Christ" (Romans 10:12-17).

Paul's point is that people cannot believe unless they are taught the Gospel. God chose to have the gospel taught by men. "For since in the wisdom of God the world through its wisdom did not come to know God, God was well-pleased through the foolishness of the message preached to save those who believe" (I Corinthians 1:21). But these preachers could not deliver God's message without being sent.

The word "sent" comes from the Greek word apostello, which means to be set apart and sent on a mission. The question should be: Who sends the preachers? The church is not mentioned in the context of Romans 10.  The word apostello was used when Jesus sent the twelve out to prepare the way for him (Matthew 10:5-42). It was also used to say that Jesus was sent by the Father, the Spirit was sent by the Lord, John was sent by God to prepare the way for Jesus, etc. I don't find it being used to discuss a preacher being sent out by a church. 

A commonly cited example is Paul and Barnabas. "While they were ministering to the Lord and fasting, the Holy Spirit said, "Set apart for Me Barnabas and Saul for the work to which I have called them." Then, when they had fasted and prayed and laid their hands on them, they sent them away. So, being sent out by the Holy Spirit, they went down to Seleucia and from there they sailed to Cyprus" (Acts 13:2-4). Notice that it was the Holy Spirit who selected Paul and Barnabas, and they were sent out by the Spirit in verse 4. The church did send them away in verse 3, but that is the Greek word apoluo, which means to be released or dismissed. The church did not direct them on where to go.

Romans 10:15 refers to the fact that people would not hear the good news if it wasn't for God sending out people to teach His message. "And Jesus came up and spoke to them, saying, 'All authority has been given to Me in heaven and on earth. Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit, teaching them to observe all that I commanded you; and lo, I am with you always, even to the end of the age'" (Matthew 28:18-20). The church supports the spread of God's word (I Timothy 3:15), but it doesn't control where the word is taught. Congregations send funds to preachers to help finance their efforts (Philippians 4:15-16), but they don't direct the preachers' work.

See “How Beautiful Are the Feet” (Romans 10:15) for more details on the work of preachers.