What is the effect of external ESD protection on noise?
You might want to be more specific, with a schematic of the proposed protection, including source and load impedances. In the absence of that, here's a start.

Any series elements (if resistive) will add Johnson noise. 

Any parallel elements (such as reverse biased diodes) will add shot noise current in relation to their reverse leakage current : assuming it's a voltage amplifier, you can translate that to a voltage developed across source and load impedances in parallel.