Dielectric grease is good for the connector and helping seal out contamination. The grease itself obviously doesn't promote a good electrical connection but it prevents tracking, shorts, etc by sealing out substances external to the connection such as water or oil. If left without the grease, oxidation occurs, water can ingress, creating a higher resistance, dropping voltage.
If you used conductive grease, you could create electrical connection between connections that are close together.
Tommyg, yes.