I can't tell if that purse has a zipper or a snap, but if the guy knows how to open it, how to put things into it or take them out, or how to carry it, then yes, of course he can use it. Nothing special about operating a purse.
Would people look at him strangely if he had one of these in his possession? Maybe. So what? If he wants to use it, he's welcome to it. At the end of the day it's still just a purse. No big deal.