Will Microsoft close an Outlook address I haven't logged into for ages?

Just make sure you actually sign in. Having the mail forwarded to another account doesn't count as activity, it has to be a real sign-in to the account itself. Set a yearly reminder if you want to keep it alive. While you're in there, check the recovery phone and email are still ones you have.

yes, they do. Microsoft closes accounts that go about two years without a sign-in, and the mail and anything in OneDrive goes with it. Signing in once resets the clock, so if it still works, log in now. If it's already gone and you get "account doesn't exist", that address is generally not coming back.