No problems. I once had a certain factory rim that developed a leak, in the rim inside area. The tire shop said I needed a new rim, which would have been hard to find. I told him to put a tube in. He had this blank expression on his face, that to me, appeared to say "I am the stupidest person, shy didnt I think of that". Ran it that way for years, no problems.
Now, most tire shops will probably try to discourage you from doing that, because of the additional work and time to mount them. It can just be thrown on the tire machine and roughly mounted, it takes a little care to not pinch the tube. Sorry for being longwinded.