I have used CT cotton thread for hand sewing my binding. I would not recommend using it for handquilting based on my experience with it in hand sewing the binding down. It tended to tangle a lot even when running it through bees wax and did fray and break at the needle if you didn't move the needle along the thread every few stitches. I have used it for machine quilting with no problems except that it left a lot of lint in the bobbin.
You can use it but I think it would end up being an exercise in frustration for you. I would spring for the heavier weight handquilting thread. I believe CT cotton is a 50 weight. Most hand quilting thread is either 40 or 30 weight. I personally prefer the heavier 30 wt.