Yes, you can in Idaho. It is a pain though. I tried carrying a rifle and a shotgun once because fall turkey season was open (in Idaho you can't use a rifle for turkeys). I was a pain, and I didn't do it again.
Leave the rifle in the truck or camp and Hunt elk with the bow. If you are lucky enough to kill said elk, and if you have the energy to keep hunting after packing said elk out, then grab the gun and go hunt the others.