Can you monitor blood glucose levels without drawing blood?

No. Blood glucose is just that blood glucose, many methods have been tried to try to aproximate that. Even with the continious subcutaneous blood glucose monitoring devices you still have to do minimum of 2 bood glucose to calibrate the readings.
No. Even with the continuous glucose monitor, blood sugars need to be checked to calibrate the monitor. The best way to asses blood sugars is to check with a glucometer which uses blood.