Bruce -

I would recommend you go very cautiously with any type of underfill material.
This poses a TCE differential situation, which could result in solder fatigue.
 Most electronic products end up with some degree of thermal cycling, whether
from power on/off or their operating environment.  The TCE of solder is
relatively low in comparison to most plastic materials, therein lies the risk
of a stress situation.
If your operating temperature range takes you above the glass transition
temperature of the material, this will further increase its expansion
coefficient.  Lastly, if your operating temperature takes you into the -40C or
below range, most of these materials will go almost rock hard, which may give
you another factor to reckon with.

If this is an absolute "must do" situation, some of the silicon gels or dead
soft urethanes might be candidates for equipment operating in a very benign
environment.  A dipped conformal coating might also serve the purpose of
coating the conductive surfaces, without full embedment of the area under the
part.  Parylene also works very well for this type task.

Good luck - Kelly

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