If you still have such a machine (preferably without any valuable data), try setting the date right before the overflow with this command
date -s @$[2**31 - 10]
and see if you can recover the system without reboot.
I have seen different daemons stopped responding and just consuming CPU, NTP clients flooding public servers, and other interesting things. I suspect many of these systems will still be running in Y2038 and that day the Internet might break.