It can be done but you should be very in tune with your rig and know what it can an can not do on this very beautiful but challenging climb. I have been over the Beartooth numerous times but have only crossed it ounce with an RV. Last year I drove from West Yellowstone to Red Lodge on my way back to MN in mr DP pulling a Jeep. I had no problem with the pass or traffic backing up behind me. I thought the road fro Tower to Silvergate was more of a challenge since there is not much of a shoulder on the East bound lane.
Most of the time that I take an RV into the park I will use the East entrance or take the Chief Joseph Hwy from just North of Cody to Cooke City.
Good luck on your trip.