I dunno, seems like "Tá luch agat agus tá cat agam" might be more effective. Y'know, or with the possessive prepositional pronouns adjusted as needed. I can't imagine "Tá potán agam" getting many takers, even if it is singular. (Also, I'm apparently twelve this morning, and can't stop chuckling over the mental image of someone trying this sentence out in a bar!)
Sadly, I don't think they're given. Which is bad for Irish, since there's a lot of idiomatic things that are normally pretty basic (have, like, prefer, etc.). If you can see people's streams, you're more than welcome to post any questions on mine and I'll answer when I can.