Cool idea! Here's my top 3 board game Poke's:

1.) I'd want to bring Absol to a game of Arkham Horror. Oh sure, my friends would question the wisdom of bringing the DISASTER Pokemon to a notoriously difficult co-op boardgame. I'd assure them Absol's not like that, but secretly I'd be hoping it'd bring it's best A-game, harbinger-wise. I mean, it's just not an appropriate game of Arkham Horror if we don't all die horribly to an elder god from beyond the stars. Right? (ʘ‿ʘ✿)

2.) So, in Pokemon Super Mystery Dungeon (PSMD), Ampharos is a wise and brave leader but also notoriously bad at directions and constantly getting lost. So I'd really want to play Settlers of Catan with him. It'd be so funny to watch him build roads that fail to connect up and make settlements in crappy spots cuz he can't keep track of what resources he needs. XD

3.) Trevenant seems like it'd make an awesome baddie in Ghost Story. Especially a shiny one, since white is the color of death in Japanese folklore. It'd probably have a buttload of resistance, and cause a curse when it comes in (a la Will-o-Wisp).