The only problem that I have ever had with putting tubes inside tubeless tires on old rims is when they are first inflated air can become trapped between the tube and the tire. This air will eventually leak out. If not through one of the rivets it will surely come out around the tub’s valve stem as it is not sealed to the wheel. Once this air is out you will have a low tire, but all the air will be inside the tube. Re-inflate to your desired pressure and you will be ok
