But ASR stands for "Anti-Schlupf-Regelung", one would not detect its absence at normal driving (excluding the warning light).
But you don't mention which car it was, S320 could be a W220 or W140 even with BAS/ASR. Does the car have a common warning light fro BAS & ASR? I did not look at W140 user manual but it could be this car then. So the light was not ASR but BAS/ASR warning?
In any case, BAS neither comes to action at normal driving. If it is ASR, you will lose slip control, that should not happen with an S320 at summer, on dry roads more than from first gear, at wet roads or quick turns you may get wheel slip easier.
If you want to get comments on the ASR hydraulic unit replacement, I'd suggest posting accurate data about the car, and possibly post at the relevant sub-section.
Yes, you are correct, the on-dash light is the combination BAS/ASR.
The "ASR hydraulic malfunction" is what the mechanic told my father-in-law (and wants around 2100$ in parts + 4h labor to fix it). I don't know the details of the diagnostic since the shop did not want to provide it (this is why I find it strange). With that kind of poor service, its unlikely that I would recommend that he gets it fixed there. He will get another scan from the "real" MB dealer and I should have more info.