Not regularly, depends on mission and duration. "Run Silent, Run Deep." One of the main points of subs is they try very hard not to be found once submerged, so anything that can provide a trail - digital, sound or otherwise - is carefully controlled or shut down. "They" have eyes and ears watching for them, as we do for theirs. One of my Navy assignments was commanding a group of ships that towed arrays looking for "sub-surface anomalies." Any guesses what fish they were looking for? [emoji16]
Your DS will be given info for both emergency contact procedure and regular communications. The spouse group often includes parents and GF/BF on FB groups and updates.
Snail mail may delivered by helos making at at-sea day drop. Number your letters on the outside, because they will arrive in batches.