No. Think of the photons as producing little pushes. When they are emitted by the LED, they produce a little push in one direction, and then the sail pushes a little bit back in the other direction.

If it were possible to create a significant volume of thrust from photons emitted by LEDs, then you would be better off just pointing the LEDs away from where you wanted to go (like a rocket).

I don't know if the strength of an LED is enough to move the craft significantly, but if it is you'd need to point it at anything _but_ the ship itself, otherwise the two forces would cancel out. Just shine it in the opposite direction of where you want to go.

No, the two forces don't cancel out, I can't remember exactly why but elastic collisions don't work like that. That's why you can point a fan into your sailboat's sail and it will still go forward, mythbusters proved it.

Mythbusters demonstrated something different, and something much less efficient than simply pointing the fan backwards like a normal fan boat (no sail required). Here: https://mythresults.com/blow-your-own-sail