I've been monitoring the focal length used in my portraits shot with 70-200 f/2.8isII over the past month and it was instructive to me that an extraordinarily high percentage of the shots were in the 120-150mm range. If this is telling me anything, it's to go straight out and get a 135 f/2...regarded by many as the primo portrait lens.
There was a small percentage in the 180-200mm range, but they were generally not the strongest shots. The virtual absence of shots from the short end says that the Canon 85mm glass would be a wasted spend.
Plenty of other photographers are fans of the 85 as their go-to portrait lens. Very few will nominate a 200 as a primary portrait lens. But hey, apart from missing the bright f/2 max aperture of the 135, a 70-200 will earn it's keep every single day that you own it.