Much like the plot of The Mystery Men, does Batman at any point in the comics let the Joker "escape" from Arkham Asylum?
Batman considers the Joker extremely dangerous so he may need a powerful reason to consider that it might be beneficial to bring him out of Arkham, and since the Joker is so unpredictable and dangerous, this hasn't happened in comics. Actually, when Batman has needed to talk directly to the Joker, he has been able to even sneak in his cell. We have examples of this from The Killing Joke to Batman RIP.
At the beginning of the court of Owls story, we actually see Batman at Arkham, fighting along side by side with the Joker. Eventually we learn that he freed him
that that joker was actually Dick Grayson in disguise, trying to gather info from inside Arkham.
So the answer is "Batman has never voluntarily freed the Joker from Arkham", much less just to create a need for himself, as in the example proposed in the question. Actually leaving him there is the only thing he can do, except for killing him, to stop him.
During the Justice League of Arkham issues as part of the Justice Leagues storyline, Batman breaks a number of his enemies out of prison the create his own interpretation of "Justice League of A", and stop an attack on Gotham. He frees Riddler, Ivy, and Ventriloquist from Arkham. But for some reason, Joker was in The Slab, instead of Arkham. But yes, Batman does break him out of there.