I use a monopod frequently but only on longer lenses, like a 200-400. I have done so on a 70-200, but I did not feel much benefit, and I felt like I lost a lot of the quick-response I get handheld. But I'm using it for action.
But you are talking about using it for
>>> taking a close up at say 1/8 sec? Or 1 sec? Or more?
I doubt, especially without VR, you will be satisfied in that realm with anything less than a tripod. I took a monopod into a cave once, trying to do longer exposures, and while I am sure it is better than handheld, it just didn't cut it for getting down into those shutter speeds. I have much better luck at those speeds sitting the camera on something - floor, a rock, etc.
I'd think of a monopod as equivalent to 1-2 stops VR, maybe a bit more if you are real steady.
Another issue if you are talking a 24-70 is you will need a ball head or similar. I shoot a monopod without -- which means I'm generally shooting without 30 degrees of horizontal, which works great for sports. The 24-70 probably means you are going to be using other angles, and the monopod becomes much less useful if not vertical (just the nature of holding it steady), so you need to put the camera at the angle. The more the angle (and your body wrapped around it to use the viewfinder -- or live view -- the less you naturally get a good steady grip.
So I'd suggest one of the light travel tripods, or even a gorilla pod (or whatever those bend-to-any-shape are) if you can get one heavy duty enough if you are trying to be in the 1/8th to 1 second range.