Yep. Even without the payoff - the blackmail immune agent is going to interact poorly with stupid blackmailer agent which simply doesn't understand that the blackmail immune agent won't pay. Or with evil blackmailer agent that just derives positive utility from your misfortune, which is the case with most blackmailers in practice.

The winning strategy depends to the ecosystem. The winning strategy among defect is defect, but among mixed tit-for-tat works great. The decision systems just tend to converge to a sort of self fulfilling prophecy solutions.

edit: i.e. there's a rock-paper-skissors situation between different agents, they are not well ordered in 'betterness'.