>> Perhaps I can set up my Gmail account in the Aqua-Mail and then create its aliases. Then, I could send from those identities, correct?
Yes.
You will need to create the aliases in two places -- in Gmail / web and also in Aqua.
In the former, be sure to *uncheck* "Is an alias" for your, well, sending alias, or else Gmail will route the alias's sent messages back to your main inbox.
I also recommend a user written guide on Gmail aliases available in this very section, they're stickies at the top.
>> Even as a reply to a message in my Exchange account?
If you also make Gmail collect your Exchange mail for you, so you have something to reply to.
>> Also, it seems as if incoming Exchange messages are not appearing in the in-box immediately. Do I need to configure that somewhere?
Sorry, that's another thing I don't have for Exchange -- push mail. I do have it for IMAP and it works with Gmail.
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But taking a step back -- most Exchange mail systems also support connecting via IMAP, and usually IMAP push is supported as well.
So perhaps you can just set up your work Exchange account as IMAP (in Aqua), not as an Exchange (EWS) account.
Then you won't have to mess with collecting it into your Gmail account, will be able to set up identities, and quite possible will be able to enable push as well.
What you will lose compared to setting it up as EWS (in Aqua) is calendar sync. IMAP just doesn't provide that.