No. Only a licensed dealer (C&R is a collector, not a dealer) may sell to residents of another state, and then only long guns.
Licensed dealers may only sell long guns to a resident of another state if the sale complies with the laws of both the dealer's and buyer's states, and only at the dealer's licensed premises, or at an organized gunshow in the dealer's state.
C&R FFLs are not permitted to engage in business as dealers, and are treated as unlicensed persons when selling (don't have to execute a 4473), and as unlicensed persons when buying anything other than C&R firearms.