By Rembrandt's time they already knew many lightfast pigments which he would have mixed himself so if the painting was stored away correctly, it could theoretically be in decent shape.

To really authenticate one would cost tens of thousands of dollars, though, so it's almost certainly not worth it unless you already have a lot of money to burn. It takes a lot of professional labor to trace the painting's provenance even if the material tests check out because it could just be some practice painting by one of his students or a really old counterfeit.