What if they did not wait?  

“And being assembled together with them, He commanded them not to depart from Jerusalem, but to wait for the Promise of the Father, “which,” He said, “you have heard from Me;” Acts 1:4

If they had not waited, would there be the church, the blessings of the words of Peter, John, James and subsequently Paul and other devout men of God?

When the Lord says, wait, many take this as a negative response. It is a blessing to be able to wait on the Lord. It means the Lord is working on your behalf. You have two choices: You can go back under the law (spirit of bondage (Romans 8:15)) or walk in the Spirit.  

“Wait on the Lord; Be of good courage, And He shall strengthen your heart; Wait, I say, on the Lord!” Psalm 27:14