Will I be able to see any sonar readings if the depth I'm scanning exceeds the maximum depth range of my Deeper Sonar?

The sonar signal has to reflect from the bottom and go back to the sonar unit in order for it to process the data - this is the way sonars work. In case the factual depth of the area you're scanning exceeds the maximum depth range of your Deeper Sonar, no sonar data will be shown and you'll see an error message "too shallow or too deep"

The maximum scanning depth of Deeper PRO and PRO+ models is 260 ft./80 meters, so they will not work in waters that are deeper than that - simply because the sonar signal does not go deeper than 80 meters and thus, cannot reflect from the bottom. 

For Deeper 3.0 and Deeper Start, the maximum scanning depth is 160 ft. / 50 meters, so they will not work in waters deeper than that.

For Deeper CHIRP, the maximum scanning depth is 100 m. / 330 ft.