I understand that Astroberry uses "chrony", not ntpd, for the NTP protocol. "sudo systemctl status chronyd" should show if this service is running.
chrony is running on my astroberry but timedatectl does indeed report "NTP Service: Inactive". I do not know why this is.
Anyway, as the regular Raspberry Pi has no battery backed realtime clock, the date would default to 1970-01-01 on power up without an NTP client running and/or without network connection.
If you have a valid date/time and no battery realtime clock added, ntp must be running
Note: commercial RPi based astrocomputers will typically add a battery backed RTC - valid date time is then no indication of running NTP. I have added a DS3231 based realtime clock to my RPi (connects via I2C). for portable, off grid use.
As for accuracy: Without NTP the RPi clock is based on the processors crystal oscillator which is not temperature compensated. Time will drift with seconds per day. The DS3231 based RTC that I use, has a temperature compensated oscillator which (from memory) should drift less than a second per month. With NTP available, accuracy depends on many factors but will typically keep your clock within 10 of ms, but may drift up to 100 ms in congested, high latency networks. If time accuracy requirements are more strict (asteroid occultation measurements?) you could use GPS as a highly accurate local time source,
If you are going to use a GPS device , please note that USB3 signals can cause significant interference with the GPS signal (just as the widely reported interference that USB3 causes with 2,4GHz Wifi). I use a GPS dongle and place it as far as possible from RPi and USB3 cabels and camera. Even then I sometimes need to disconnect my USB3 camera to get initial GPS lock - but that is topic for another discussion.