Yes of course, have the AI write the agents.md file which the AI can then use to make changes to the project. This of course works better than just having the AI write changes to the project directly.
I do not, but I don't do that for LLMs either. Conventions and documentation I write and present are as succinct or lengthy as they need to be, no matter if the recipient is human or machine.
I mean I had my LLM generate most of my AGENTS.md, and I tweak it maybe once every week or two. It's minimal investment, and it's a gift that keeps on giving.