Safe to exclude capacitor in this circuit?
C2 and R16 appear to be designed to isolate the power rail from LED switching transients.

The question is why would they do that? I doubt the transients from switching a few LEDs would have a significant impact on a typical digital power rail. 

Maybe the power rail is shared with some analog audio circuitry (or fed from a rail that runs analog audio) and there was a percived need to avoid injecting audible spikes.

Another possibility is that this was done to reduce electromagnetic emissions from the cable connecting the display board to the rest of the system or maybe to reduce crosstalk issues in that cable. However the capacitor doesn't seem the right type for that, a big electrolytic is more likely aimed at noise in the audio band.