My guess is that if the database is subject to auditing then LLM access (obviously writes in particular, but even reads come with exfiltration risks) will be a hard "no" and instant red flag. When it's a person, there is a sense of accountability and opportunity for remediation.
I suppose that LLMs will be treated as a code artifact and liability will shift upstream towards who deployed/approved the access in the first place. Even though code is essentially deterministic, making that association fairly simple, it's going to boil down to this same paradigm.
Perhaps governance rules will evolve to even explicitly forbid it, but my gut feeling is that for what the future determines to be "practical" reasons (right or wrong) LLMs will warrant an entirely new set of rules to allow them to be in the chain at all.
+ EDIT: both my wife and I have experience in this area and the current answer is companies like KPMG don't have an answer yet. Existing rules do help (e.g. there better be good documented reasons why it was used and that access was appropriately scoped, etc), but there is enough ambiguity around these tools so they say "stay tuned, and take caution".