Yes, they do.
What do they do when not repelling boarders? Storm Troopers are on Naval Vessels, and are the one truly reliable resource a Commissar or senior representative of the Imperium's forces has.
There's a relative lot of information about Naval combat in the Gothic War series.
Why on Earth would an Imperial Guard
unit have any authority on a naval vessel? There has been a strict distinction between the Imperial Guard and Imperial Navy since the Horus Heresy.
And what else would Storm Troopers do on a naval ship while in transit? Anything else an Imperial Guardsman is supposed to do: pray to the Emperor, maintain his kit, drills, and try to pass the time in any way (drugs, gambling, ect.) they can without the commissars jumping down their neck.
I myself have not read the Gothic War series. I'll probably go out tonight and snag myself a copy of them. In the mean while, please cite where Storm Troopers are the go to men in standard
naval circumstances. Nothing out of the ordinary where their unique skills are required (say, assassinating the leader of a shipwide mutiny). Something mundane that MP are expected to do. Manage the loading and off-loading of gear, checking for contraband, operating and guarding the brig, and routine security checks.
Because from everything I've read so far, Storm Troopers are not used for these menial tasks.