An application in principle is documented proof that a lender is willing to provide the loan you need for your mortgage. An AIP is not a guarantee that someone is going to lend you the money for your mortgage - it's simply a note that says you are eligibile.
You can ask your lender for one to prove you are eligible - they will ask some basic questions and perform a credit check. If it's a soft credit check, it will have no effect on your credit. If it is a hard credit check and your application for an AIP is turned down, your credit score could suffer slightly.