Yes, Server can be ran as a service.
You can follow the link below to download the Noventri Server Service Installer:http://www.noventri.com/forum/NoventriServerServiceInstaller.msi
Once you download the msi file, go ahead and un-install Noventri Server.
Next, install the Noventri Server Service Installer.
After the Service is installed, go ahead and re-install Noventri Server as you had it before. Start Server, and make sure that the "Start Automatically" is not checked. Then, you can close Server and start the Noventri Server Service from the Windows Services window. You should not have the Server logo (orange gear) in your system tray.
Thank you, and let me know if you need any assistance getting it up and running.