I've got various ancient GPS receivers, usually as modules rather than complete devices.
Most of them are fine with the one or two rollovers they've already seen. Some work OK once given the current date.
They all tend to give accurate position and 1pps signal (if present) - it's only the UTC time they get wrong, and then it's out by exactly 1024 weeks. The actual GPS calculations are all done using that 1024 week cycle and UTC time is just a spinoff.
Some roll over at a date that isn't at the 10-24 week epoch : they know the data can't be before they were built, so anything in the earlier part of the cycle is automatically considered the 'next' cycle. I think NTP (where it's using GPS time as a stratum 0 reference) also adds the 1024 weeks if the receiver is giving it a stupid date.
There's a good chance there will be no problem on anything but the very oldest receivers, and if you do find one reading wrongly, set the data manually (if that's an option) - it may work it out.