My Radio room dwellers are staying at a really low level and not gaining any xp. The four of them combined haven't gained a level since release. Is it intended that the radio room has no co gains?

no it doesnt.. neither do any of the special boosting rooms as they are there to raise stats not level...

however the radio room is still really important as it not only brings in new people.. but it also increases happiness for everyone in the vault which makes everybody more productive.