No. Windows Server 2019 is not a listed supported operating system.
Supported Windows Server versions are: Windows Server 2008, Windows Server 2008 R2, Windows Server 2012, Windows Server 2012 R2, and Windows Server 2016.
If that didn't clarify: The system requires a specific driver. An unsupported OS will have no compatible driver, leading to failed installation or erratic printer behavior.
Heads up: Attempting to use an unsigned or generic driver may cause system instability. For the latest compatibility information, always check http://support.brother.com/.