While technically it's perfectly possible to do windowless, display server less off-screen GPU accelerated rendering with OpenGL, practically it's impossible these days because you need a display environment to actually get access to the GPU. Fortunately the structure of graphics systems is changing these days (Hybrid graphics, display compositors). Already Mesa provides an off-screen context creation mode (OSMesa), but it's far from being feature complete.
So right now, you'll need some kind of display server drawable to work with on which you can bind a context. X11 offers two kinds of GPU accelerated drawables: Windows and PBuffers. You can use FBOs with either (PBuffers are technically Windows that can not be mapped to the root window and have an off-screen canvas). The easiest way to go is to create a regular window on an X server but not showing it; you can still create an OpenGL context on it and create FBOs, like shown in numerous tutorials. But for OpenGL to work the X server you use must be active hold the console and be configured to use the GPU (theoretically with newer Hybrid graphics capable X servers and drivers it should be possible to configure the X server to use a dummy display device and configure the GPU as a secondary device for accelerated rendering, but I never tried that, so far).