I tried my ancient Garmin eMap a couple of weeks ago - before the epoch rollover. I haven't used it in years and it say with no batteries. It figured out where it was quickly enough. But the date it showed was in 1999. Note this was even before this week's rollover - must be a very old GPS! I used to carry this one when flying as a backup navigation device, since it has a built-in database of towns roads etc at the "right" level of detail. But nowadays Tophat on my smartphone is a much better backup.

My Garmin 76s is not quite as old. I had it stored with no batteries for years. Turned it on a couple of weeks ago and it took an hour to figure out where it was. But then it showed the right date. Stored it with batteries until trying it again yesterday, it got a fix in a few seconds and the date was still correct.

Ah, wasn't saving a bit or two in the data packet worth all this trouble? :-)