No, it will stay there forever.
I know what you feel about those worthless erc20 tokens that were sent to you. But you are free to create a new wallet that you haven't posted anywhere so that there will be no airdrop tokens.
I can relate on this. I have bunch of worthless token on my stash, some were from bounty and some from an exchange where it loses its value overtime until it was delisted.
Is there anything one can do with useless ERC20 Tokens? For example, a discontinued project or a bunch of scam developers.
I think there is none but just lay it there, if your garbage token is too many I would follow what eagleman said, create another erc20 address for your valuable token.