No. Typically you have a six (6) month grace period from your last day of attendance (regardless if you withdraw, graduate, or get academically dismissed) before you begin any payments for loans.
Payments for loans will not be to the school, but to a loan servicer that is randomly assigned to you (Examples of those different loan servicers you can get assigned to are: Navient, FedLoan, Great Lakes, Nelnet, etc.).