Apologies for going OT, but is GW ATP a leftover from the installation under British Rail? I was under the impression that it is mandatory for all rolling stock on the line.
GW-ATP is mandatory for operations over 100mph on the GWML where ATP trackside equipment is fitted (so between Paddington and Bristol via Box) - the only exception is Class 220/221 operating between Reading and Didcot. When the Airport Branch was constructed it was decided to install ATP from the off, and extend the implementation to T5 when that extension opened.
As the branch, and only trains to operate on it were fully ATP fitted, Railtrack/Network Rail decided TPWS was unnecessary, and it wasn't installed. As such, the 332s aren't TPWS fitted either (they can't get anywhere not ATP-fitted) - the 360s were delivered with TPWS as it was a requirement for new stock by the time they were introduced.
While the Paddington to Hayes bit of Connect could be covered by 387s, the 387 wouldn't be able to go into the airport branch, as it doesn't have ATP. Terminating an up-direction "connect" at Hayes involves an unacceptably long dwell in the Up Relief platform while it turns round, head ways are pushed in the peaks as it is.
On top of all that, the 5-strong fleet of 360s is worked hard as it is. Connects require 3 units, and a 4th (usually 205) is used in the ITT (inter-terminal-transfer). 332s are only permitted to operate DOO with platform dispatch staff, CD and RA indicators - which prevents them being used on Connects as cover. You could however get away with a 332 on the ITT.
Thus, in theory, you could just about scrape by with getting rid of 2 360/2s, but any failure in the 360 fleet would cripple the connect service.