A DirectAdmin license only affects the DirectAdmin service itself. If you cancel the license, everything else (web, e-mail, databases, etc.) keeps working as it always did. You only lose functionality of the DA service.
The DA service is more than just the GUI, so there might be some side-effects. For example, DA manages the automatic SSL certificate renewal for all your domains, so you would have to self-manage this to prevent surprises. There would be no more automated backups. There might be other quirks, as DA performs various tallies/cleanups, so if you have any kind of limits set, it's possible they would not properly count/reset, and you might experience some form of downtime (or at least inconvenience) until you figure out what's going on.
There could be more quirks. This is just a few examples of what comes to mind.
In summary: Yes, everything will keep working, but there may be future hiccups that require manual maintenance by you.