Depends on the specific person and the severity of the moodswings. Its hard to say with me because some of the hard to categorize dysphoria may be neurological but I have experienced standard rapid cycling as well. That new anti convulsant that has been found to be of use as a mood stabilizer for me in experimental usage has shown great promise but the Clonidine patch has stopped working and I've had to add (with permission) a pill of it a day which has made me a bit sluggish. For myself before my recovery from psychotic symptoms and after, the standard is that every so often I had to change mood stabilizers although for a while they were quite effective but I don't believe this to be uncommon.
Well when I was on medication I believe it just made them less severe. It made them much more bearable and brought them down to levels where I could cope with them much easier, but I still noticed that every once in awhile I'd be feeling down for no reason or I'd catch myself talking about weird things loudly to my friends.
But definitely much more bearable.
For me they mostly take away the severity of the mood swings. I still have them on a regular basis, just not as bad. Or, if I want to get technical, on the days when I'm experiencing dysphoria the medication can make me feel a sort of fake happiness, if you will. Or sometimes it makes me even more depressed or irritable. Depends on the day. It's why meds are so tricky.
Meds also made my mood swings much more manageable. And while they didn't disappear, I was much more functional. However there is something else that helped too. The fact that I was actively taking a pill twice a day gave me a sense of empowerment: while it didn't fix everything, it made me feel that I was helping myself. There are no guarantees that you're meds will work the way they are supposed to, but there is a good chance that something out there will. And it is always a positive feeling to know that there are lots of options and opportunities out there to treat a condition. That includes medication and other things too.
My pdoc kept saying I had opposional defiance disorder because I would disagree with everything she said-the main thing being that exercise would NOT improve my mood swings. I was wrong, she was right. I started a simple walking program, 3-5 days a week, and that made a big difference in the way my moods cycled. Everyone's different and I don't know if it's something you have already tried, but if you haven't it's something to consider. Like what aqua was saying, it gives you a goal, and a sense of empowerment. Especially once you've reached your goal.