Maybe. The last time this happened, apparently some devices got very confused about their ephemeris calculations when the week counter rolled over and started looking for satellites that weren't in view while ignoring the ones that were, meaning that they lost GPS lock completely. There's also some complication with the individual satellites having counters that roll over at a very slightly different time from the main GPS week counter. Devices doing a clean start after the rollover completes should be able to navigate but with a wrong date.
Also, all modern devices are meant to be able to handle the week rollover properly so long as it's less than 1024 weeks after the firmware was built. So it's mostly a question of what interesting bugs they have in their handling of it.
Biting the hand that feeds IT
