Well, it's a good idea on paper. PUN ALERT!
According to Gaming-Age, the newest Nintendo retailer catalogue mentions an upcoming set of Mario Party cards for the e-Reader. It seems these cards will contain multiplayer mini-games. Presumably the games are small enough to be sent from one GBA/e-Reader combo to other GBAs, just like a "single-cart" multiplayer GBA game.
It's currently not known how many players these games will support. Multiplayer card games aren't even feasible on the original Japanese e-Reader model; a pass-thru port for the link cable was added for the American and subsequent worldwide releases.
No release dates or prices are mentioned in Gaming-Age's article, so stay tuned for further info.