Actually he look quite a bit like this guy.
As to the OP - I think if Neanderthals had survived into the relatively modern era, it would mean they’d overcome whatever it was that made them extinct in our reality (and currently, climate/habitat change is a favourite explanation) so their chances of continued survival would be as good as any other small tribe - I don’t think, had they survived, we’d really make the distinction between H. neanderthalis and H. sapiens before modern genetics - at least, I doubt Linnæus would have, if we could interbreed successfully.
Holy CRAP! It’s Chuck Norris!
{looks like Duckster (my cuz) also agrees}