Maybe. A very important question is why do you have severe osteoporosis at such a young age and what can be done about it. There are new developments in osteoporosis treatment including a new understanding regarding vitamin d deficiency, and newer medications for building bone (forteo). Osteoporosis and running will require a fine balance. You are at increased risk of stress fx or pathologic fx.
Too much impact. Why do you have osteoporosis at such a young age? Has this been investigated? You should focus on low impact aerobics such as exercise bike or elliptical. Weight bearing exercise as well such as light squats and leg presses to strengthen the muscles around the hips. But keep the weights light!!
Low impact. You are at an increased risk for fracture. Try aquatics, body weight, or resistance bands/ tubing biking, and/or elliptical. Aquatics allow you to perform body weight exercises, but being in water actually reduces the stress on your body due to buoyancy. Once you are able to perform body weight activities then look to add light resistance w/ bands/ tubing.