Drew a quick plot to show the trend the diameter could experience over time. Explained what all parameters would have an effect on this trend (volume-vs-diameter, elasticity force of balloon, flow rate through orifice, etc.) and how each parameter would affect the trend line.
The atmosphere on Mars is 1% as dense as Earth's atmosphere at sea level. Given the lack of atmosphere, and with no modifications to the drone, I would say that the drone wouldn't even lift off the ground. In order to get the drone to fly, the blades would have to rotate faster or they would need to be bigger.