Don't know how densely populated your airspace is or whether the ground sensors are Mode S or ATCBI but when traffic density gets to a certain point the ground sensor can't handle all the target replys and correlate them with primary returns and pass athis data to the ATC facility to be used to make the display for ATC to look at to separate you. If things get a little bad it is just a time lag. If it gets more bad the targets can coast or start just giving up trying to correlate everything. The worst case the tracks are dropped and the data is dropped and the screen goes blank.
That said, it is very difficult to make a light GA operator spend that kind of money on a Mode S transponder unless he needed a new one anyway. Check with AOPA, they have a very decided opinion.
I believe the TCAS/ACAS will give you better RAs with Mode S in the other fellows A/C and will get a better RA on you if you have Mode S too.