sorry for the snark, but what would your wife rather your kids be? shallow, peer-pressured, follow-the-crowd sheeple who only care about what others think of them?
Given that this is the "cool" way to be, and playing Pokémon isn't, I'd venture a guess at the answer being "yes, with an if, or no, with a but."
Though really, if I had kids, I wouldn't want them associating with D&D players either (going from the OP's comment about "socially-awkward, gencon-attending, D&D-playing, girlfriend-less geeks"). D&D is a terrible game, and I'd impress it upon them as much as I could. I'd want them playing a
good RPG. That said, I'd also be trying to get them into Magic instead of Pokémon, but I wouldn't say "no" to Pokémon so much as, "well, have you at least taken a look at..."
But seriously, Pokémon is
never going to be mainstream "cool." If you play it straight and unashamed, you'll get respect out of anyone you really want respect from. You're never going to get respect from jocks or airheads, but then again you don't
want their respect. The animé is truly godawful crap and goes a long way to maintaining the image of Pokémon as for kids and losers, but then again, a lot of the players do too. Especially the players that try and be "cool" about it. Acting ignorantly "mature" does not earn you respect. Quite the opposite. And it hurts the image of Pokémon quite a bit, too.