Yes it is physically possible to make the AR10 (or any repeating firearm for that matter) full auto. In the USA and elsewhere there are legal constraints against it though, with some exceptions.
Possession of a class three firearm depends upon your locale. Some states don't allow the peons to even own a class three firearm. IIRC somewhere on the NRA's website there is a breakdown of what states' allow what. The BATF should have something similar somewhere on their site also.
Many countries don't allow full auto firearms by civilians while some have very lax legal restraints.
Also there is a link on Tom Bower's board, http://www.subguns.com to firearms law.