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Will your benefits cover the full cost of your schooling? They can certainly ask that you show ability to pay the required tuition and fees. I don't see any reason why they couldn't require you to fill out the financial aid paperwork as well - the school may need to report how many eligible students they enroll for isntance, regardless of how many students actually utilize a particular type of aid. If you don't want loans, don't sign the prommisory note for them - but that is different from filling out the FAFSA or some type of questionaire for your school's aid department.
Im not sure of the rules of your school, but as long as you have the ability to pay their should be no problem. Typically what happens is when you enroll in school they send off a letter to the VA to verify you are enrolled and attending. It is only then that you receive payment for you GI benefits. Those payments usually start the 2nd month of enrollment. There may be some confusion however. With my situation, the VA pays the school... Then I get paid as well. Thats the way the Post 9/11 works. The money you are paid is the E-5 housing pay. However the financial coverage for the school itself is paid directly to them. Talk to financial aid and verify this. They may not have experience with this setup. Especially if they are a technical school. Let me know if you have any other questions.