This doesn't specicaly answer your question, but you have a large camera and lens combination.
You might want to consider a lens tripod ring that will allow you to rotate the lens and keep the weight centered over the monopod; otherwise you will be constantly trying to keep the monopod from falling over.
I have two monopods... one with a ballhead on it, the other without.
The ballhead I use is a modified Manfrotto 308RC... this has been superceded and I think the most similar current model is the Manfrotto 492. This has a single lever to lock or release the ball, and no panning axis (that's not needed on a monopod).
I've modified mine by replacing the quick release mounting platform that was on it with a basic Kirk or Wimberley like this...
... which is compatible with the Arca-Swiss style lens and camera quick release plates I use on all my gear. This type plate and platform allow sliding the lens forward or backward a little as needed, for better balance.
IMO this ballhead is plenty sturdy for 70-200/2.8L. I've occasionally used it with 300/2.8L IS or even 500/4L IS, though I usually prefer to use a tripod with them. I regularly use the monopod and ballhead with 100/2.8 USM macro, 180/3.5L macro, 70-200/4L IS, 70-200/2.8L IS and 300/4L IS. The cameras I use most often on it are 7D and 5DII, all fitted with battery grips. No problem handling lenses and cameras in these sizes and weights.
Which 70-200? The f4 is about 2/3 the size and weight of the f2.8. 60D with or without the battery grip? You might be able to use a little smaller ballhead or tilt head, if you are using 70-200/4 and 60D without the grip. But the Manfrotto 308RC isn't all that big, though it does turn my monopod into a potential weapon!
Note: the 100/2.8 macro and 70-200/4L lenses don't come with tripod mounting rings, but I've added them to each of my lenses. I believe they both use Canon Ring B (black on the macro, white on the 70-200, of course). The 100L uses Ring D.
Yes, it would work fine with 70-200/2.8L IS II. That lens is the same size and weight as the first version of that lens that I use, and similar to my 300/4 IS. I've used those and larger lenses on it without any problem.
Just to be clear, if using a ballhead or tilt head with an Arca-Swiss style quick release platform, you also have to install an Arca-Swiss style lens plate on a lens such as yours that has a tripod mounting ring. This is an example of this type of lens plate...
If using another lens without a tripod ring on the camera, in order to mount it on the quick release platform you need to have a camera plate installed. Below is a camera plate especially for 60D without vertical/battery grip (a different one is needed if using the grip)...
The Arca-Swiss style is the most versatile system of quick releases and especially useful that it allows some adjustment of lenses for better balance, but it does add some cost. You also could choose get a ballhead or tilt head like what I recommended that doesn't have a quick release, that simply screws into the bottom of the lens or camera. Use that as is or add a quick release to it later.
I basically use the same setup. Like Alan, I have two monopods... one with a ballhead and the other without. The top of the monopod often has a reverseable bolt. Cameras use 1/4"-20 threads, but tripod heads use 3/8"-20 threads. So the tripod and monopods usually have either a reverseable bolt or a swappable bolt (and come with both sizes).
For monopods, I prefer the flip-lock levers. This is because if you're using a mono-pod, you're probably moving frequently and need fast setup/collapse times. Flip-lock levers are faster, but they do require some "maintenance" (you have to adjust the tension on them so that when you flip them to the "lock" position, they've got enough tension to keep the monopod from slowly sliding down. They usually include a tool that lets you adjust the the tension nuts (which are usually "nylock" nuts). Before any important event, check the tension on the flip-locks.
I use a Benro B2 head ballhead. There are B0, B1, B2, and B3 sizes (some vendors call them BH0, BH1, etc.) There is actually a B00 size as well. The larger the number, the more beefy the head. The B2 head is appropriate for a DSLR with a decent size lens such as a 70-200 f/2.8.