Nope. What will happen is a retroactive gag order - serve a warrant that orders that the service provider to refrain from having disclosed its past nonexistence. Or orders the service provider both to refrain from disclosing the warrant's existence now (by withdrawing the canary) and to tell the truth, so that the provider is in contempt either way. The law doesn't require logical consistency!
And authoritarian thinking doesn't require logical consistency, either; in fact, compartmentalization of thinking is one of its hallmarks. The 'time travel' and 'Morton's Fork' versions of the warrants will be perfectly accepted by the authoritarians, while the 'actively lie' version might not. The trick with the 'Morton's Fork' version is that the argument to the court (and to public opinion) can simply harp on how evil (whichever course of action was taken) was, and ignore the fact that the same argument could be made against (opposite course of action).
It's just like a traffic cop waving a truck into a 'no trucks allowed' lane, and then ticketing the truck for being there. (Happened to my brother. The cop admitted in court to doing just that, and the judge essentially said to my brother, 'bad day for you that you were there in the first place. Guilty.')