I suspect the results would be quite poor. Incandescent filaments increase their resistance when they get hotter, so driving them at constant RMS voltage means that the power will decrease as they heat up, which will give them a degree of stability. At constant current, though, the power will increase with increasing temperature.

(Of course, they’re quite hot and radiative cooling increases like T^4, so this isn’t necessarily a show stopper. But it’s probably not helpful.)