I think it depends of the client's implementation.

PoW (NIP-13) is already implemented in Nostrudel, but unfortunately just for publishing. It does not show messages mined above certain difficulty. If clients implement it properly, the user will be able to control the quality of messages it will receive.

Obviously it does not block anyone from annoying you if you are an specific target, but for random/general spammers it should work well.

Im using 20 as difficulty of my posts for testing purposes.