I would say no because it is on a busy narrow road but maybe other people can weigh in... However, the good news is that you can do plenty of power walking right on the resort! There is a lake/pond with an asphalt/dirt track around it...about 1/3 of a mile for a loop. Also, CSS is on the edge of cliff and there are lots of steps to walk. I run about 6 miles most mornings and never find a need to leave CSS.
There are paths to walk or jog around the lake area. The beach is much too small. I would not walk off resort only because it would be along the roadside and that would not be too safe. Jamaicans may be rather laid back in general but not when driving a car. They seem to want to be where they are going...NOW!
The jogging path around the pond is beautiful - views of the hills and ocean. If you combine that with climbing stairs, you will get a great workout. There are no sidewalks on the street near CSS, and while others have jogged that area, why risk it when there is a beautiful path at the resort?