How Does Increasing Digital Gain Affect Noise Results?

Increasing gain increases both signal and noise. It may sometimes increase SNR, but it's unlikely to make much change in DR. Generally, if you are in the regime where you are shot-noise limited, you can improve matters with gain. However, given the multiple noise contributions, you will have to perform the experiment to determine what the ideal gain is.

A basic equation for SNR of a detector can be found here: Shot noise.