EG - Your ROTC scholarship is not in jeopardy because you indicated you would not be applying for financial aide.
Nearly every college and university has a need-blind admissions policy - the box is there mostly so they can get you on the list to send out financial aide information. Many times financial aide deadlines are prior to acceptance notifications.
Now - you can still apply for financial aide so long as you comply with the deadlines.
While a ROTC scholarship is not considered need-based aide - it is still financial aide. It is counted against the costs of attending.
Actually, would I even be eligible for financial aid?
This is determined by your parents income, the costs of attending and the school.
A piece of unsolicited advice for all -
Anyone applying to any civilian school (unless maybe they have a 7 figure trust fund) should at least apply for federal financial aide by completing the FAFSA.
Several reasons -
Even if you are accepted to an SA or receive a scholarship you should have a back up plan. Think about what would happen if you blew out your knee and didn't make R-day or you lost your ROTC scholarhip because blowing out your knee kept you from passing the PFT.
You could be stuck with a nice tuition/room&board bill.
For ROTC scholarship winners, you still probably have a room/board bill and completing the FAFSA makes you eligible for very low interest loans.
Unless you are prepared to write a check for your college expenses - think of it as another "insurance policy".
And yes - your parents must complete and sign their part.