The only limitation, so far as I read, is that they can only have one STAB per type. If you only want to utilize one of those two STABs, then so long as that's the only STAB of that type, it should be fine.
Firstly, Jeri is choosing to borrow their tier (ie. STABmons), which means he's also borrowing their base rules (eg. banlists) as well. Ignoring some of those (eg. unbanning) means we aren't playing in that tier at all, while imposing more just defines his challenge (eg. one STAB move per mon per type, UU/RU, etc)
Unless I miscounted, Vulcan has 74 OU-PU to Gaia's 102 (excluding same-tier formes, megas). Additionally, you have near-identical tier-by-tier quantities (Gaia less one in RU) until NU/PU, where Gaia overtakes Vulcan by far.
Now, I'm not exactly the most active in these threads, but I don't really ever hear Vulcan complaining about having a low amount of pokemon to choose from.
EDIT: Case and point on Fairy + rare types: http://prntscr.com/butc04