The last time Valve ever released a demo for one of their games was way back in 2009, for Left 4 Dead 2. One year earlier, they had brought Portal 1 to the XBox Live Arcade as “Portal: Still Alive”, and as all XBLA releases require that a demo trial be offered alongside the actual game, they had been forced to release a free trial for it (not all XBLA trials are time-limited, though).
Since CS:GO will be a download-exclusive game, one could only assume that this would also be the case for its XBox 360 version. However, some code found within the CS:GO beta seems to imply that its free trial won’t be limited to the XBLA, and it also seems to confirm that CS:GO will be a paid release.