what happens to timed schedules if internet drops?

[cherwilco]

I have about 70 ws-8-150's on camera towers connected to the internet via pepwave cellular modems. I use a poe power tap to power the pepwave from port 2 of the switch and I have that on a scheduled off for a couple of minutes every morning.... causing my cellular connection to get a hard reboot once per day. what happens if the internet fails and NTP in the switch can no longer get the date and time? does the switch keep counting time until the next ntp ping?

btw I also use ping watchdog to reboot port 2 incase of failure to ping our vms server but I have seen more than once where a cellular connection is just barely alive enough to receive pings but not good enough to allow me to remote into a modem to manually reboot....