Self-Hosted Main

(Sorry for the incredibly noob question. I'm trying to figure what is possible before buying some parts, which is why I'm asking instead of just trying it out myself.)

I am planning to make a server out of a few old PC parts. I'll mostly be using it for two purposes:

(1) Serving media, cloud storage and a few other services to my devices.

(2) As a media center for a home cinema setup.

Of course, since (1) implies it will be running 24/7, I'm trying to be mindful about power consumption. One of the ways I've planned to do that is by keeping the setup headless until I actually want to use it as in (2), when I'd like to be able to launch a graphical session (for the sake of the argument, let's say in Ubuntu).

Now my question is: is there any way to launch an X session (again, simplicity, let's say I plug in a keyboard and type a command) and exit it without needing to restart the server? For example, if someone else is using the server to watch something in their own laptop, I wouldn't want to restart the server just to watch something in the home cinema.

My intuition tells me that simply running startx should not kill the existent session, is this correct?