Not really. Although there is a way to have Aqua *not* remove messages deleted from the server...
But I don't recommend doing things like that.
Aqua (and other mobile mail apps too) is designed around "cloud sync" where the app is a "window" into your messages on the server.
In that respect, it's not like desktop mail apps (Outlook, Thunderbird) which often download messages fully, don't need anything on the server after that, and happily operate without a network connection even.
