Would this be the correct way to wire this breakout board sensor with an ADC?
First, the point of the breadboard is so that you don't have to solder.  But you will have to solder hookup wires to the ML8511 -- connect the male ends of those into the breadboard.

The UV sensor needs +3.3V and GND for power.  Connect the EN pin to +3.3V unless you want to be able to put the sensor in sleep mode.  You can probably connect the OUT pin to any of the channels of the ADC -- channel 0 would be typical.

Also you should put a 0.1uF capacitor between VDD and DGND and another between VREF and AGND to reduce noise.