The definitive answer will require the MSDS for the paint. I suspect it will work but you may run a health or laser damage risk.
True anodized aluminum is both a color and a protective layer. The dye is impregnated into a layer of aluminum oxide that protects the surface from corrosion. When the laser is applied to the anodized surface, it ablates the dye, leaving behind the aluminum surface. This would do something similar but the paint would act like paint, not anodizing, and could chip and flake. The lasered area will also be lower than the paint, leaving a rough surface.