You know, I have never subscribed to that project of painting porcelin, tubs or comodes or sinks. It just does not work UNLESS done by a professional that does a super job of preping.
I would not do a think if my short term plans are to gut the room anyway. You will be throwing money down the drain. If it did not stick before, why will it the next time?
Secondly that fake tile board is NOT intended to be near or around water. It is only wafer dust glued together. I would, since we are talking short term, go out and buy some plastic white corner molding that you can liq nails to the fake tile around the tub and mitre the corners and load it up with silicon caulk and then you have a good patch job. The plastic molding will act as a water barrier and shed water off. The molding should be about four inches tall.