Got several different answers over different calls today.

Does having an in-cabin pet attached to your res force the system to skip over you in the queue (even if there are no other pets in the first class cabin)?

2 agents said yes, system will not allow an upgrade to a passenger traveling with a pet.
2 agents said yes, but only if there is already a pet in first class (limit of one in F). Otherwise, upgrade will process as usual.