I'm a college student that hates relying on caffeine to keep me awake (although, that's not been the case lately since it's finals season...). So what I used to do on nights I stayed up late studying was take a quick 20 minute run around my neighborhood. After that, I'd be pretty pumped up and studied well.
The number one fail-safe method that makes me fall asleep? Reading in bed. Especially something boring. If I combine that with some Natural Calm magnesium, that'll pretty much knock me out.
So I guess I'd say no don't exercise if you want to fall asleep.