No, the generator is only for the house. Same setup as at our old property in that respect. I'm going to use simple "cheap" drop ceiling tiles to line the upper perimeter---same stuff that was stapled to the ceiling at the old shop. That's just one piece of the sound mitigation...there will hopefully also be baffles and other sound absorption up in the truss area, too, and maybe some creative wall hung things. I have a lot of scrap trim boards from the house that was demolished next door that I can employ to make stuff like that.
Here, that's done by alternating circuits...duals are not so common, at least in existing homes. But yes, using a double pole breaker or strapping two with appropriate hardware, can keep things safe. I might consider this in the shop, but I only have a few instances of quads planned. I really don't need them other than for charging, etc.