Would they want to know that? Probably not. Did he try to tell them? Probably. Did they instead shoot the messenger? Almost certainly. Did that drive him to publish and be damned? Possibly. We'll never know I guess, but it's a well trodden path with plenty of footfall to this very day
Chugalug2
You are of course correct and many whistleblowers do so only once they feel they have run out of road elsewhere. Part of the weakness of Enigma lay in the fact that whilst the Germans had very good technical knowledge that allowed them to develop the kit in the first place, their crypt-analysis wasn't up to the same standard as either their technical capabilities or the capabilities of Allied crypt-analysts; as a result, they never fully understood the weaknesses of their own systems right to the very end of the war, thus enabling its exploitation.
Now that said, I think there are some instances, probably including this one that a whistleblower has to either circumvent the blockage in the chain of command or simply sit on their hands if they genuinely believe there to be a major operational weakness. If you do nothing publically, there is always the chance that the enemy hasn't yet worked things out for themselves and you buy yourself a bit more time. But by going public, all you are doing is guaranteeing that the enemy now knows your gaps and weaknesses.
With the luxury of hindsight, and had he not done so already, might it have been worth a letter direct to the Chairman of the JIC or even the PM's office if he felt so strongly rather than going public? At that point, with his reputation still intact, a man of his calibre would still have the credibility to make such senior people take note.
Even if you have no interest in WW2 or codebreaking, the whole Welchman case makes for an interesting discussion on the relationship between operational security, ethics, courage and values and would, I think, be an interesting case study at the likes of IOT and the various Staff Colleges.