No. I think he will want to, I think he probably already wants to. But I think the other high-ups in Russia know that the rest of the world won't stand for it. He keeps saying that he doesn't want outside interference in Ukraine, but using nukes will cause just that because everyone will feel like he has to be stopped immediately before he nukes anyone else.
Putin's forces sound like they're already having a harder time in Ukraine than expected, so it wouldn't be smart for him to bring even more enemies into the conflict than he's already struggling to deal with. Right now, the threat of nukes is what keeps other countries from joining in against him. Once he uses nukes, he's played that card, and then other countries will feel like they have to go in, because it will be all or nothing.