As in legally? ethically?
Yeah, the "Grand Salmon" is a coveted Middle-Main combo. Several threads on here about "turning the corner". I'm jealous. Have an awesome trip.
Only trick is getting the two to coincide. You might end up making a long final day to get on the Main trip soon enough..or camp at Corn Creek for a night or two if you have time to burn. Hitch to town and stock up on beer, or coordinate with one of the shuttle outfits for a resupply. Blackadar will do food packs.