you could in theory, but I dont think its effective and wouldnt recommend it..
Some impurities might be trapped inside crystal lattices, so a wash of the crystals wouldnt be as efficient as redissolving in non-polar and washing that. Also, hard to say what "brown" is, because it could be a number of things depending on what plant you extracted with what chemicals (and their manufacture impurities) and method to extract and how clean you worked.
And no, lye would NOT dissolve in naphtha, so you could simply do a Re-x as per FAQ, and any lye or polar impurities would stay on the bottom with the goo.