I would never use them to write a proposal from scratch (as in "write a grant proposal to submit to call X on topic Y"), but they can very effectively turn informally-written lists of bullet points with (human-generated) ideas into well-structured sections of flawless, effective text describing the ideas in detail. As well as iterate on the text (make this section longer, shorter, add idea X, emphasize aspect Y more, etc.), suggest risks and contingency plans, make a Gantt chart, etc.
All this represents the overwhelming majority of the work (in terms of hours) in writing a grant proposal.
It will still take a lot of time to write down the bullet points and get the data in support (I suppose that nih grants work like the ones in my country). The people that propose 40 grants in a year and that are targeted by this rule do not just use AI for helping to redact their proposal.
As a funny anecdote and a side note, I noticed a pattern of tricks used by people to detect AI texts that is dangerously close to my natural writing habits in English. For example I've seen people saying text with a lot of "fancier" words ( closer to my native language than more natural words), using a lot of moreover or "-" in the sentences. They are all things I've read people here and elsewhere say it helps them to know that a text is AI generated. I'm now very self-conscious about using moreover.
All this represents the overwhelming majority of the work (in terms of hours) in writing a grant proposal.