Here is a shot I took last year of what a lot of lobstermen do in Maine when they leave their boats on a mooring. The far aft placement of a relatively large sail does a good job of keeping the boats pointed into the wind. However a lobsterboat has relatively little superstructure to catch the wind, so the sail is quite effective (I was told). The simple mast and boom is easily stowed (or taken ashore) when the boat is working.
The steady sail that can be mounted on the mast and boom of a typical recreational trawler is mainly effective at looking cool, if you're into that sort of thing. According to people with GBs I know that have and use them, they reduce the hunting on a mooring or at anchor to a degree, but they don't reduce it enough to make a huge difference. The mast on a typical trawler is not mounted aft enough to make a steady sail truly effective, particularly not the small sails that will fit the typical "trawler" mast and boom.
The people I've talked to who use a steady sail to reduce yawing on a mooring have told me that a stern anchor actually does a much better job. Which is what we use when necessary.
As to damping out roll in a beam sea, sure, they'll have some effect but again, everyone I've talked to who has and uses a steady sail has told me that in terms of damping roll, they don't contribute anything noticeable. They can, however, put a tremendous strain on the stays and mast mounting hardware to the point where I've talked to a couple of people who had their whole mast toppled on a windy, big-wave day on the Strait of Georgia. The stays and hardware on the typical "trawler" mast are strong enough to support the mast and maybe a 200-pound dinghy but that's about it. So if one is contemplating using a steady sail to dampen roll in anything other than a ight breeze and small waves, it would probably be a good idea to get a good analysis of the bracing hardware's ability to stand up to the load.