All RF lenses are focus-by-wire. I don’t have the 24-70/2.8 IS yet (mine arrives next week), but I have the 14-35, 24-105/4, 70-200/2.8 and 100-500, and FTM works on all of them even without the half-press.

I suspect you have electronic manual focus disabled in your settings. On the R, it’s in AF tab 4. I use back-button AF. I keep mine set to magnify, FTM works if I just pick up the camera, and if I’m pressing AF-ON and turn the MF ring the view magnifies at the AF point.

Also note that FTM doesn’t work during active Servo AF.