If my eyes are working right, the part is the ferrite choke filtering the 3.3v feed to the analog supply pin (VDDA). It's purpose is to keep high frequency noise on the digital supply isolated from the analog section of the uP. You could verify that the board still works by replacing the broken part with a wire temporarily -- provided you have the skills and tools for such work.
Yeah, the ADC will work if you just connect a wire between those 2 (extremely small) pads. In some cases the ADC might have a little more noise on its measurements.