For example... If I had a 2W green laser, a 2W red laser, and a 2W blue laser, could I combine them using crystals to form a 6W white laser? Or is that now how it works? If not what would be the output in watts of such a laser?
You would have 6 watts of total power, and the color may appear white to a human; but "white" is not a wavelength. Nothing special would happen to the light where the beams overlap, and the fact that your light sources are lasers wouldn't matter.