Yeah, it can, but you’ll need to mark your AA guns somehow as they are now Power Dependent and you’ll have several more lying around on the map.
Though I’d suggest you go to the trade thread and ask for just the 2nd Map and extra AA guns, you should be able to get them for $10ish +shipping. That’s what I did.
you don’t REALLY need to mark AA ownership. It’s rare indeed for Japan to combine AA with Germany, or US to bring AA to UK, etc etc etc. Since they never can attack, they’ll never share a space with an opposing force. So I don’t see this as being that big of a problem.