You can, but if you have any condition, it's best to check with your doctor before starting any workout. I think you are referring to type II diabetes, but I may be wrong.
Blood glucose level and fat are 2 different things. Even though inter-conversion happens between them, as body undergoes its natural process of gaining and shedding fat, losing fat and lowering of blood sugar levels are 2 different things.Check with your doctor the ways to maintain sugar level while working out.
Muscle building is a good idea as muscles feed on calories, but at the same-time, you'd need calories to build muscles. If your condition makes you breathe heavy, gives you dizziness and you don't feel easy during workout, then talk to your doctor about it. Also, always have someone around, or notify the gym authorities about your condition, so that they will be aware.
I'd not suggest doing any high-intensity workout.