Normal sailing requires the ability to "tack," or move against the oncoming pressure of the wind, or in this case the solar wind. But "tacking" requires another force or friction, such as that of the sailboat hull and keel in the water. Such forces are not available in space, so "tacking" in space would be impossible.
The original Bajoran lightship, that Commander Sisko worked hard to duplicate, from an 800-year old blueprint would never have been able to achieve escape velocity from the surface of the planet Bajor.
At around 34 mins, Ben and Jake sit at the front of the ship near a nautical gimbaled compass. When the ship suddenly rocks, the compass begins to wobble on its axis; however, it is clear that actor Avery Brooks purposely bumped the compass with his right hand to initiate the wobble.
Captain Sisko speculates that the rapid journey to Cardassia is made possible by the solar sails capturing faster-than-light tachyon particles, in addition to the expected solar wind, thereby achieving "warp speeds." However, even in the universe according to Star Trek, no ship can exceed the speed of light in normal space. Warp drive operates in part by creating a warp field, or subspace field or bubble, around a ship, which bypasses the speed-of-light limitation. However, the Bajoran-style sail-ship did not have a warp field generator. Therefore, even if the sails had also been able to capture tachyon particles, it would not have been able to achieve warp speed.
While tacking in space is almost certainly impossible (since there's no opposing force to give leverage) the sails are filled as if the ship were "running with" the solar wind. If they were tacking the sails would not be filled from directly behind.
The solar sails presented in the episode are far too small to propel even a small vessel in space. Real solar sails would have to be many kilometers/miles across to pick up a usable amount of energy, and very lightweight compared to what is shown. The sails shown in this episode appear not much larger than would be found on a similar-size sailboat on water.
The solar-sail spaceship could not have taken off from the surface of Bajor into space, using the sails. No mention was made of how this was done, and for such an evidently primitive culture, it isn't likely they had suitable rockets. Further, even if the Bajoran sail-ships had been able to reach Cardassia or some other planets, they would not have been able to land and then take off again for a return to Bajor.
Sisko mentions adding an artificial gravity net because he isn't comfortable in zero gravity, but the ship is otherwise designed for zero g. The winches and cranks would be very difficult (if not impossible) to use without gravity.
In Star Trek: The Next Generation Episode 3.6, Chief O'Brien claims to have built ships in a bottle for fun after Captain Picard asks if anyone else has done it. In this episode, he scoffed at the idea that Commander Sisko was building an actual Bajoran ship for fun. Considering that he's an exceptional engineer, one can assume that someone forgot his character's history.