I do not have more than one amp on a single circuit so I don't really have experience with that but TheOrganDoc is correct in saying that it should not be a major concern unless all channels are driven at high volumes.
Even though Emotiva claims a 10 amp requirement for the UPA-7, I believe that figure has a bit of a safety margin. The theoretical capacity of a 15-amp circuit is 1800 Watts so two UPA-7s (875 Watts each) on a single circuit should be fine. Any more than that (or the addition of a sub) and you will more than likely blow the circuit at some point.