I'm pretty sure that the limits on number of pets per cabin would still apply. The question really is, are the AA systems smart enough to block your upgrade, or might you get downgraded at the gate, having lost your chosen Y seat, landing into 31E or something like that.

I do know that if you have a pet noted on your reservation, you are prevented from using OLCI, for example.

It's relatively rare to see any pets in the front cabin (IME), so I maybe wouldn't be as worried about that as I would be about seat assignment - GLD upgrades are the last to clear, which means there's a good chance you may end up in the bulkhead (where pets are not allowed), with no other seats open.