If this is a temporary solution until you are able to get carpet, then I would not personally worry about etching the floor. You just need to have the expectation that at some point moisture could become an issue with older concrete, which could potentially lead to the paint popping/peeling.
If this could become more of a permanent solution, then removing all the current coating and etching would be ideal. The process of etching removed any sealers currently on the floor and provides a slightly rough surface for the paint to adhere to. Since this floor is from the 20s, I highly doubt its as smooth as a babies bottom. If you were using an epoxy floor system, then I would strongly recommend etching as a bare minimum.