I have a cheap keyboard, plastic unweighted keys, that I used for some technical practice. It's a bit... shot. Plastic keys can wear out, yes. But if it's a cheap keyboard... bang away. Your playing is more important than a keyboard and you don't want to adjust to a flimsy light keyboard touch. Play it like an acoustic.
I looked into replacing the keys once, but that was more expensive than just buying a brand new cheap keyboard. Plus the springs and rubber garbage can age and weaken eventually.
I wouldn't too much about damaging the keyboard. It gets used. It's aging whether you use it or not. It's there to be played and will eventually wear out.