Yes, but that would be a lot less efficient. With a dielectric mirror you can get easily 99.9% of the maximum momentum gain from the light, while with a solar powered laser you would get for the emission the compounded efficiency of the solar panel + storage + laser, so way below 10%. So you would gain around 10 times more impulse from your solar panel absorbing light than from the actual laser.

The final momentum gain is a bit different as the maximum you can gain from a photon is double its momentum (because you can reflect it back with opposite direction).