Sorry, I misunderstood your question. I thought you were asking about the situation when the sync via the specific connection channel is disabled at the system level.
But then I am confused by your question:
"When Aquamail is set to autosync but the wifi or data is disabled, does it preform the autosync anyway".
Obviously, it cannot do any sync if there is no network connectivity.
So, I am guessing, you might be asking if Aquamail wakes up to attempt the scheduled sync.
Yes, Aquamail must wake up, because if it were sleeping, Aquamail would have no way of finding out if the network is available or not. If the network is unavailable, it cannot perform the sync, so, it goes to sleep until the next scheduled time (or other event configured to start autosync).
Also, based on the permissions, I am guessing that when, say, Wi-Fi is turned off, Aquamail may try to turn on the Wi-Fi (if that is enabled in Android settings). -- This is a standard behavior for many Android apps.
If you want Aquamail prevent from trying to sync, you need to:
1. Turn off the Scheduled Sync. The master switch is Settings -> Mail, receiving -> Scheduled Sync = OFF.
2. Turn off Push. The master switch is on the same configuration screen, "Imap PUSH" (or Exchange Push).
3. Turn off sync on events. On the same configuration screen, under "Event type", uncheck all events.
I hope this answers your question. If not, please clarify your question.