The answer is "kinda"
If you put an off the shelf map onto an AEB/AJL, then added (for instance) an intercooler, the ECU would detect the cooler intake charge and increase the power by itself.
If you changed the exhaust, then you'd gain in terms of spool times, but not power due to the way the ECU works.
If you changed the turbo, then in reality you need a remap to get the most of it, however you dont NEED one. Mark (Byzan_A4) is currently running an AJL with an upgraded turbo, injectors and MAF, however hes running the stock map. This works due to some maths mark and myself worked thru which basically means the map has been linearly scaled by 38%
The AJL/AEB ecu is a bit odd in that it doesnt have a boost sensor, it bases everything on MAF value, but this makes it quite easy to fool the ECU in the way that Mark has. Basically by fitting a larger MAF, you effectively scale the ECU's internal maps by the % increase in MAF area, and so long as you match the MAF increase with a similar increase in injectors, the fuelling will be more or less fine. That ofcourse doesnt address ignition timing, but it will work ok so long as you dont go too far, running super unleaded and letting the knock sensing system deal with things.