yes, the rocker arms can become worn, but maybe the tips could be re-dressed, if necessary.
If you are getting new pushrods, first make sure all of the valve stem tips are at the same height. Hopefully, when the heads were done the machinist was careful to grind the valves and seats consistently, so the stem tips end up at the same height, so you can get one length of pushrods which will fit all the valves correctly.