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.