Foremost makes ducts for underground use. Fiberglass or plastic. With
a long duct run, especially with part of it underground, it is not
likely the heating air would be very warm when it got to the far end.
Smae problem with cooling air, it would not be very cool.
Also, it is not likely you would get enough air. Sounds like you would
have a lot of pressure drop.
I would try a high sidewall register on the inside vertical wall
blowing towards the outside wall(s). With proper register sizing and
proper duct sizing, this would be much more doable with likely much
better results for comfort. Your contractor should measure air flow
with a flow hood when he is done. Also be sure to put at least one
return in the addition.