If the state picks up a vehicle theft charge can it be pursued if the alligator refuses to go to court

By alligator, I assume you mean the person making the allegations (not called an alligator).    The State's Attorney has the power to issue a subpoena against this person.    A subpoena is a court order that directs a witness to show up to court for a court date at a specific place on a specific date and time.  Then that person, if called to the witness stand, is to tell the truth to all queations posed.  If that person fails to show up, then there is the issue of the witness being found in contempt of court, which can mean fines and/or jail for the witness.  Over the course of my career, I have had too many people tell me that the defense is that the witness isn't coming. This is always a bad defense strategy.  If the State's Attorney wants to win bad enough, they will subpoena the witness and then seek its enforcement if the witness declines to come.  I would get a good criminal defense lawyer to map out a good defense for you.  Good luck to you.