If connecting the AR to the main out on the rear of the 1080 and the speakers to the AR you're only using the AR as the power amp so only 60watts/channel.
The amplifier in the 1080 could still be used to drive an additional set of speakers but not the same pair so no the outputs of the two are not really summed the way you might be thinking.
For instance, I've used a Kenwood KA-7300 to drive the mains, with a second amp with its own gain control connected to the 7300 to drive the rear lanai speakers.
So I have the 65watts of the 7300 for the mains, and the 34watts for the lanai but both are not cumulative into one load.
Hope that makes sense lol.