In theory, it sounds like it's possible. You click say: A Gui and then Boom! It prompts you to join a clan. or a community, or whatever, But I've yet to find any API for it. So that begs the question, is there one? And where can I find it? Once I know where to look I'm usually all set
So something like:
game:GetService("MarketplaceService"):PromptPurchase(plr, id)
get's turned into
game:GetService("GroupService"):PromptGroupJoin(plr, groupId)

2 comments
I don't believe you can join groups in-game yet, would be a nice feature though.
Sadly it is not possible, but the way you described is pretty creative.