It can clog the filter to some extent and if not too badly to run the engine, fresh fuel "may" help clean it back out. The larger issues aren't the replaceable filter but rather gumming up a carb or injectors or even a pressure regulator. Again new fuel (or fuel system cleaner) may help to clean them out, but again the engine has to run well enough to get the fuel through to do that.
IMO, not worth the risk/bother unless it's hairy situation where you need to get out of dodge because the natural disaster +zombies are hot on your heels, and that's all the fuel you have.