Tricky. As the tracker is a real 'interloper', I would expect it will have no action on any part of the A2 system if taken out.
This is not advice, but if it was my car, after disconnecting the battery, I would take note of the tracker cabling (colours etc), and cut the cables with enough length to be able to rejoin (highly unlikley to need to), and insulate the ends of all wires attached to the loom.
I would then plug in the red connector, reconnect the battery, and see what happens. I would expect all to be well, but the keys may need reprogrammed as per the instructions up the thread.
However, you will need to make your own decision......
There are some real experts on this site, so others may have a more professional suggestion.
Or go to an auto-electrician and spend the bucks!
Very interesting problem you have. I wonder if there is an aerial somewhere also, as where the tracker unit is located, I would be surprised there is any coverage.