Sure, you can play it with a joystick, but it won't work like you're actually flying it with your joystick, as the only thing you can actually control in FL is where you are shooting. As the closest thing you can get to flying with a joystick is using it as a mouse, you'll just end up with a rather wierd way to control your ship, as it won't work like you'd be used to in a flight sim/spaceship sim.
tl;dr: No, not really. I wouldn't recommend it, at least.
EDIT: If you do want to give it a try, you could use this or any other free joystick-to-mouse software.