Sure you can. We would just never recommend it - whether it's in your condition or a solid state. You are in need of a replaster. Paint is a very temporary, low grade fix. It will quickly start to fail and chip off, even more so with compromised plaster.
FYI, painting will increase the cost of a replaster. The prior owners painted my pool at some point and I'm paying for it $$$$. It doesn't last and will leave your water super cloudy every time you brush it or rub against it.