Technically yes, but it’s currently unsupported.
Enzoic can be installed on machines with Windows Server Core. It should install and run like any other Windows software. However, with that said, Enzoic needs a UI in order to be configured and managed. There is no way to edit settings, through the command line at this time. Meaning at least one machine in the domain needs to have a non-Core Windows server OS in order to function.
In addition to this, Enzoic for Active Directory is not tested or quality checked for Windows Core, and therefore is unsupported at this time.
If you have an environment that has some Windows Server Core machines, Enzoic should install and run just fine (given that you’ve set up the configuration steps on another machine first). But because this is an unsupported OS, if you do run into issues, there is very little that support is going to be able to assist with.