Not when you're in the 10th swarm in and it's still eevee...I only wanted one of each eeveelutions. when i had five i was worried that they might not show up again, but now i just wish some other pokemon like sneasel would show up (stupid me entered sneasel as a tester during the first day).
If that's in the main game, it could be rigged to only have eevee swarms. On the other hand, I've heard that when you evolve an eevee for the MC you get an eevee swarm soon.
I had a single random eevee show up in one location. There was an announcement that it was there, and IIRC there were several other indigenous pokemon there as well. This was probably right after I evolved my eevee.