Probably not. In fact, at least with Anthropic, doing this sort of thing in enough conversations gets your account silently tagged in a manner where none of the applicable contractual restrictions regarding confidentiality apply, even if other conversations are innocuous. This is assuming ZDR is not enabled. You can see evidence of that in Anthropic's "Detecting and countering misuse of AI: September 2026" report. Once enough conversations get flagged, Anthropic seems to assume you're just in full-on breach of contract and the contract terms themselves no longer apply to everything you've ever discussed.
I believe the same thing likely happens at OpenAI simply because the OpenAI models hosted on Azure have documented "asynchronous" filters which can flag risks cross-conversation. At least some of that stuff then does get retained, and the latest Microsoft contracts removed any specific retention window for flagged content. Again, assuming MAM (Microsoft's "ZDR") is not enabled. This type of architecture at Azure probably didn't arise in a vacuum. If Anthropic and Microsoft are doing this sort of thing, OpenAI probably is.
Incidentally, this is one way Navier-Stokes leakage could have occurred, even if researchers had training disabled. Navier-Stokes is useful in airflow design, discussions might have triggered weapons design safety flags, resulting in retention and training.
Incidentally by design, I'd bet. "Ooo Lean! Terrence Tao could be trying to break RSA or elliptic curve cryptography! /s" Conveniently for the PR team, we need this data to train on to make sure America has the biggest and best math.