Off the top of my head I want to say not without some machine work. Rosko whould be better at answering this as he has both in his shop space right now, but he is...ahem...on vacation.
As far as I know the cb360's engine was a "clean sheet" design from the 350 it replaced. I know the motor mounts are different, and there is very little that is shared (maybe some tranny parts on the early 360s). I don't even think the bore and stroke on those engines are the same. I know the cb360 jug won't bolt up to the cb350 head.
Since the cb360 was not as fast as the cb350 and the aftermarket supports the 350 but not the 360, I think it is probably a better bet to get oversized pistons and bore out your existing cylinder. Stay away from the 360 parts.
back in the day when i knew nothing i bought a cb360 at mid ohio for $50.00! i got back to the pits and c. marshall took a look at it and said what are you going to do with that. i said, use some of the trick parts from it on my cb350, like the six speed gearbox. he said, nothing matches up, just throw it away. i said, but i just paid $50.00 bucks. i hauled it home and there it sat, till one day when i........yep, threw it away.
Its not quite true that nothing matches up between the 360 and the 360. The valves and I think the valve springs are the same. I think the oil slinger thingie this the same too and possibly the starter motor. Otherwise they don't share anything that I've been able to find.