Hi Derek,
Thanks for contacting Syncfusion support.
Yes, Essential PDF will be working in Linux docker container using ASP.NET Core. We have attached the sample with docker support.
Please refer below links for more information,
Docker for windows can be downloaded from below link,
Switch between Windows and Linux containers:
From the Docker for Windows menu, it is possible to toggle which daemon (Linux or Windows) the Docker CLI talks to. Select Switch to Windows containers to use Windows containers or select Switch to Linux containers to use Linux containers (the default).
To enable docker support, select the Enable docker support and select target OS with Linux.
George