Ive heard anecdotal stories of dielectric grease reducing or preventing good contact. In some cases with thin, flimsy pins or something like that, I could kind of see it... But for most uses, I cant.
The actual contact surface in a connection is a small fraction of the actual surface area that is "touching". The Nye graphic shows it well. The use of the term "surface asperities" is correct.
For batteries, where the terminals are way spaced out, and there isnt particularly high voltage to begin with, I prefer a conductive electrical grease. I use NO-OX-ID. I apply it around the metal to plastic bases, and then a thin coating on the terminals themselves. Then Ill generally wipe a very thin coating on the upper exposed surface.
For any connector where there is the potential for potentials of different types in close proximity (such as in a harness), I like a thin coating of dielectric grease. I also like dielectric grease on the seals to help them avoid sticking.