I think the idea that he got Nayuta killed by turning into Chainsaw Man assigns more agency to Denji than he actually had at the time. He did declare in himself that he wanted to be Chainsaw Man (ch. 150, p. 7-8) despite deciding to abstain from it for Nayuta's sake, but he's also being actively cornered into becoming Chainsaw Man by the Chainsaw Man Church ruining and actively endangering his life.
Public Safety wasn't going to protect them. Never mind that they can't efficiently fight against weapon hybrids and were constantly playing catch up in regards to the CSM Church's activities, the agent assigned to Denji fled from her job when it came to actually fighting. Twice. Turning into Chainsaw Man, regardless of his desire to be, is currently practically necessary for his survival.
(On a side note, it just sunk in that Barem's the first male to manipulate Denji's life for Chainsaw Man-related purposes...)
Since the-- no, the nervous breakdown fully happened before the handjob, when he collapsed in front of a collapsed brothel and followed Yoru into an alleyway to get castrated. If anything at all, the handjob and makeout session slightly improved his mental state by emotionally fulfilling him.
...there's a non-zero chance that they'll struggle with Denji not going black Chainsaw Man because they don't know that he still has at least a smidgen of happiness from the handjob.
There's a non-zero chance that their plans will be impeded by an amputee handjob.