I have seen cypress pots before but I can't remember where. As a wood I believe it's very inconsistent due to various factors. Some of it feels like balsa wood and some feels hard as heck. I have a cypress scratchbox from Tim Sanford that looks and sounds great also.
the different densities in the wood is exactly why it would be a good candidate for stabilizing. Below is an owl and pot call I did from some figured ash. Dyed and stabilized green. The dye and resin goes into the soft wood, making it hard when cured. The hard wood resists the resin, remaining untouched, producing some very unique color combinations.