No, you shouldn't offer animal protein to your Russian tortoise. Some species of tortoise, mostly forest tortoises, eat animal protein and fruit, but not Russians.
Some species, like red foot tortoises, need more protein in the diet and eggs are one way to provide that. Most of us will not recommend feeding eggs to weed or grass eaters like russians or sulcatas. I don't think a little bit once in a while will do any harm, but I don't think it would do any good either. This is a point I've been pondering for a while...