you can shoot carbons from a traditional, but the thing you should be concerned with is the draw length. You shouldn't have the same draw length on the trad as you do your compound. most trad shooters I've seen and talked to only draw the bow to thier chin and nose. I imagine your compound anchor point is further back.
I suppose on that note, your arrow on the compound may have a stiffer spine than would be required for that particular bow. You might have some strange flight issues.
The trad folks tend to shoot a much heavier arrow too. Met a guy who added weight to the front of his arrows to pull the slow flying arrow and hit harder.
My brother in law is shooting my old Easton Axis from his 45 lbs trad bow. They fly pretty good for him.