Yep, I recently did this. My main is on Bloodhoof raiding while all my alts are on Steamwheedle Cartel doing more fun things. My main, however, was the one that had them, so I had a friend on SWC invite me into a group via RealID. I purchased and opened the Sumprush Rodents, and they were on SWC; after I left group they all despawned from my perspective. A guildie on SWC headed there after we had ended the group and she was able to get one.
I believe the key is who is Group Leader to determine what server you're on in a cross-realm group.
Also, there is no CRZ for Pandaria. And you don't really need to be all that concerned; the pets respawn repeatedly during the timeframe (altho one has to be captured/killed to spawn another; forfeiting causes the same quality to respawn) and there's about 8 or 9 up at a time. But if you really want to be sure no one will be around ... do it the night the Patch comes out.
EDIT: Because there's a timeframe, make sure you keep the first one you fight regardless of quality. You don't want to go rare hunting, not find any, and then realize you didn't grab any when they all despawn.
Quick and Dirty Primer to Raiding With Leashes II:
Chess Event Strategy/Discussion: