What would happen if you put in for the transefer, but leave before it clears?

You will have violated your probatoin, you can be arrested and put in jail.

you will have violated your probatoin, you can be arrested and put in jail.

Even if I'm in another state?

Yes, even if you are in another state. You did not have prior written permission to leave the state your probation is in therefore you would automatically violate that probation. Ask prior to leaving or you will be violated.