You're likely to be able to get the funding through the school for your materials for the drone, you'll still be getting credit towards graduation, and you won't be doing anything that might be illegal with financial aid money.
I'll add that a professor who might be even remotely associated with the field may know people at other institutions or in industry. This could pay off down the line when you are looking for employment.
Also, if it's school sanctioned the IRS won't even blink at letting you write off costs on your taxes (or parent's taxes, if you're a dependent).
Also, if you have an active IEEE or ACM branch at your school, they might have additional funding if you can get enough people and a faculty member or two on board. We provided funding to a couple projects, one was the SECON robotics competition, but I vaguely recall helping with some other project(s).