dielectric grease is used in layman's terms to prevent dielectric
corrosion.  that is corrosion between two dissimilar metals that have
different voltages of reduction (that is a physic/chemistry term).  when
dissimilar metals have different reduction voltages one can oxidize the
other, oxidation is what is commonly referred to as corrosion.  in
addition to oxidation by other metals oxidation can occur from other
atomic elements such as chlorine as is the case with salt compounds.

if oxygen is excluded from the metals by the use of a coating whether that
be paint or grease no oxidation can occur.  that is why dielectric grease
is used.

okay onto the part of the question that asked about electrical connections
being hindered by the grease.  all electrical connections rely on physical
contact ie pressure to work.  the 'best' electrical connection in simple
terms could be thought of as a bolted connection.  that connection type
gives very high pressures, most hight voltage stuff is of the bolted
connection type.  a bolted connection is not always practical in economic
or physical terms.  another method of electrical connection is a spring
type connection.

if you have ever been in a circuit breaker box that doesn't use screw and
the breakers just pop in it is because a spring finger type connection
system is being used.  push type connectors used in the vanagon system are
of the same spring design.  lets take the case of a normal 1/4" male and
female blade connector.  the male part is of a fixed dimension.  the
female part is constructed from a spring type material.  when you push the
two together the female part made of spring material expands over the male
blade.  the connection here is made metal to metal with the pressure
provided by the spring.  the spring is the sole clamping force for this
connection.  if you have adequate force by design at your connection it
will be strong enough to displace any grease and the metal to metal
connection will be made.

spring connectors are subject to problems when exposed to high heat.  this
is why it is bad to reuse connections that have been overheated
electrically.  the heating changes the springyness of the connector and
thus the clamping force of the connection is reduced.  this often can lead
to a poor/loose connection and arcing at the connection site.

those are my thoughts for what they are worth please take them as a
starting point for your further research.

jonathan