Nope, you can only get your PAC from your current provider, so no way to get it during signup anyways. You will need to ask for it while terminating your old contract. You probably don't stand much chance of getting a number back after you drop it.

You may want to check if the company you are going to have any cut-off period after the start of a contract to accept a PAC code. I can't think of any good reason for one to exist, but many things defy explanation.