When the last rollover occurred (1999?) GPS units were rather less common than today, but there were a few where I worked for surveying and laboratory timing.
As I recall, units fell into 3 categories :-
1) No effect, continue operation as normal
2) Loss or degradation of time signal (and therefore probably position) until the ephemeris data downloaded from the satellites is all updated. This takes some minutes.
3) Total failure

I only saw one unit which was affected, and that was total failure. The assumption was that the firmware rejected satellite data claiming to be timestamped before the firmware build date. I don't recall the type, but it was an old unit even then.

I suspect the number of unit types which fail this time around will be very small.