First off, it's not FAFSA. That's just the federal aid application. You'll be signing the note directly with the Department of Education, who is the lender, not the school, even though you will be receiving any money you are borrowing above tuition and fees as a refund from the school.
My understanding is that you CANNOT sign for multiple schools, since you can only attend one school at a time and that school needs to certify your attendance for you to receive funding, which goes through the school.
As far as I know, nothing is "binding" insofar as you would owe nothing until funds are released. Once funds are released you ARE responsible for repaying them, just like with any other lender. If money is released to one school and you decided to switch to another, you'd have to figure out how to get that money refunded back to the Department of Education, less whatever they would keep as their cancellation fee. You would presumably then owe accrued interest and the origination fee that was deducted from the loan disbursement, and then reapply for new money at the new school. I don't think there is a mechanism to transfer money, once disbursed, from one school to another, but I could be wrong about that.
For this reason, and because I'm not sure whether or not you'd be responsible for multiple origination fees if you had to apply for multiple loans, I'd hold off on signing the note until you are sure you won't be switching schools (i.e., you have selected CTE at your final destination, or at least have a pretty clear indication that your WL call won't be coming).
TBH, you're most likely worrying about nothing, because whatever moves you are going to make are going to happen before you will be FORCED to sign the note. Beyond the deposits, which will be non-refundable after 4/30, no money should be due until shortly before matriculation, which should give you adequate time to make whatever moves you think you might be making. In case you were unaware, the vast majority of WL action happens in May, and orientation doesn't begin until July/August.