It can tell you which ancestral population you come from decently well, not totally accurately - on 23andMe "French & German" is a group but has really poor recall, and "Latin American" is not a group nor "Aboriginal Australian" despite how possible they look.

But that's just clustering and it would work on any random groups you chose. In particular, it would still work if they picked a group where none of the members were related to each other (and indeed that's how it works now). As long as you're related to one of them it'd still be able to show you're a member of it.