Which error?
That would be a massive overhead. Also, it wouldn’t achieve what you might think, since the update check of course has not finished yet when the banner is shown. … I mean you could trigger it as foreground task via /etc/bashrc.d ordered before dietpi.bash, which shows the banner. But then you would need to wait for the update check + in case APT update check on every single login, before the command prompt appears.
If it really is important for you to see available updates ASAP after a reboot, and if it is a headless system, you can order dietpi-postboot.service to start after time-sync.target. But check whether chrony.serviceis pulling in and sorts itself before time-sync.target, else this wouldn’t have much meaning. If not, there is a systemd-time-wait-sync.service, which primarily waits for systemd-timesyncd.service to finish the actual sync (just like our run_ntpd), but its manpage states that it works with other time sync daemons as well, just not as reliable: systemd-time-wait-sync(8) — systemd-timesyncd — Debian trixie — Debian Manpages