With the VW OEM audio head-unit, you just pull the head-unit with the stereo removal tools from the DIN slot. Of course, once you've pulled and subsequently re-installed the audio head-unit, you'll need to enter the radio-code to re-enable the audio head-unit. No need to disconnect any battery connections.
With an after-market audio head-unit, the question largely comes down to one of, "does the audio head-unit use the OEM wiring-harness plugs to attach to the speakers/antenna/etc.?". If the answer is "yes", then it would likely behave like the OEM audio head-unit.
As to being able to use the AC/audio with the center-console cover removed, the AC should be fine (the buttons/switches/etc. will still be in-place). Using the audio system would likely be problematic since the center-console cover provides physical support for the DIN-slot that houses the audio head-unit.
Good luck!
