Can I ski Nordic backcountry skis at a resort?

Technically yes, but it is not recommended for several reasons. Nordic backcountry skis lack the width, stiffness, and edge hold for resort skiing at typical resort speeds and terrain. Free-heel boots provide minimal ankle support compared to alpine boots. Most importantly, many resorts do not allow free-heel skiing on their slopes for safety reasons, and you would be a hazard to other skiers due to your limited speed control and turning ability. If you want to ski both backcountry and resort, consider an AT touring setup that can handle both, or maintain separate equipment for each discipline.