I'm not a lawyer, so I can't authoritatively speak on this, so this is just my understanding. I'm generally going to stick to the conservative side here, so that even if something is likely legal but untested, we should draw our metaphorical line just a little closer to "definitely legal, widely accepted".
In several jurisdictions, purely LLM-created content has been deemed not copyrightable, not creative work, so as you don't own it, you can't license it as Apache (or anything else). Our policy is to be Apache v2 licensed, so adding other content to the project could cause more headaches than it is worth. So no, purely LLM-created content probably can't be permitted.
Another area we need to take care is in our JRE emulation - it is my understanding that we should not accept LLM contributions in this area, since it runs a fairly high risk of reproducing code from OpenJDK or other non-apache licensed JRE implementations. Outside of that, it is my personal belief that LLM usage in moderation may be safe to accept.
I think there is a lot of good prior art in conservative LLM policies out there that we should draw on when building our own policy. I think that the above constraints (subject to my own, possibly flawed, interpretation of the law where I reside) are clear from existing policy, but stating them outright might help to have specific guidelines to point to.