I'm wondering whether atmospheric pressure (high or low) would have any impact on the favorability of hydrostatic skeletons. Obviously hydrostatic skeletons work well in water, but I'm not sure if a gaseous medium would have different effects. Could anyone give any physics-based insight on this question?
The "hydrostatic skeleton" idea basically revolves around using incompressible fluids (usually water) to maintain a structure, like in big trees or hemichordates. In fact, as silly as it sounds, mammalian penises, including those of humans, are hydrostatic organs, and use the same concept to remain stiff even under pressure. It's especially useful in high pressure environments, so you're on the right track.
Essentially, the idea is that if you don't have some sort of pressure on the inside pushing out, then the big outside pressure will squish whatever needs the skeleton. Generally, for things like organs or creatures, being squished isn't great. But water, which can't be compressed, essentially acts like a brace: it's really, really hard to squish your organ or creature if its skeleton is hydrostatic because water "tubes" inside the skeleton exert an outward pressure of almost-equal magnitude. It would take an extremely large amount of pressure to crush a creature with a hydrostatic skeleton; in fact, the pressure would be great enough that the creature would've died of something else (like suffocation or incineration) long beforehand.
If you're evolving life on a planet with high atmospheric pressure, and big oceans aren't viable for life (so that creatures don't choose the evolutionarily-easier path of just growing gills), then a hydrostatic skeleton might show up at some point.