Re: will I have a problem if Nine isn't the one syncing
Hmm, I really don't know how it's going to interact, sorry.
Actually here is another idea -- what if rather than accepting your invite inside AquaMail (in the email message), you open the event in your calendar and accept there? Will that send a response for you?
I recall there being some difference (with accepting an email message vs. the actual calendar event) in Outlook for Windows, and IIRC, when I tried it in Aqua, it worked the same way, so it looked like Exchange server logic.
Sorry this wasn't recent and I can't be more specific right now, but it might be worth trying (perhaps with some test event).