I never used the SAC myself, but I presume it'sacting as astandard Intel AMT Serial-over-LAN software terminal. You are correct, once most OS's load (Windows or Linux) no more serial data is sent to the terminal console. At that point, you need to use RDP or VNC to take control of the machine.
Note that while the OS is loaded, the Serial-over-LAN feature is still avaialble thru a COM port (Generally COM3 or COM4). So, if an application where to send data into that COM port, it would show up on your terminal. In Linux, it's pretty simple to launch on startupa console that redirects the input and output to that COM port. In Windows, you could write an application that makes use of the COM port.
Hope it helps,