Short answer: Yes.
I was a little disappointed with my first experience with infant swim lessons. There are some programs that start at 6 weeks old and involve the baby swimming underwater right away. That is what I was expecting. Unfortunately, most swim classes seem to start at 6 months old and are less about actual swimming and more about getting the baby used to the water and ready to learn how to swim. That said, there was a huge difference in quality between the two classes I took. The first class was like free swim with your baby. There was very little instruction, very little group activities. They had some rubber duckies to throw and let the kids go after them and the teacher would take each child and swim around with them once during the class, but I felt like there should have been more.
With the second class, there was more. We sang songs, chased floating toys, practiced skills together (blowing bubbles, getting face wet, kicking, reaching, floating), and talked about water safety including, teaching the babies to climb out of the pool and wait on the side. The teacher was very active and gave the parents a lot of information. Both classes were only 30 minutes (babies can't take much more than that), but the second class was so much better. Of course, the second class didn't really teach Ian to swim, either, but laid the groundwork for him to learn.
A few things I learned:
1. Be patient. It will seem like your baby isn't getting much out of it, but all of a sudden things will click. Just trust the process.
2. Don't push your baby too hard. It should be fun. Push them gently. If your child is screaming, they will not learn. Your pushing may backfire and they may become afraid of the water. One example: I tried to blow in Ian's face and pull him underwater. That was a suggestion in the first swim class. If you blow in their face, it is supposed to cause them to hold their breath. It just made Ian furious. After doing it once or twice, I realized that I needed to relax about it. So instead, I started to let him slip a bit and get his face wet, but not go under. One day, when he was 9 months old and we were at the outdoor pool at the Marriott in Cairo, on our way out of the country, he was holding on to the side by himself and he let go. I let him go under and then pulled him up and he wanted to do it again. Then we tried letting him sit on the side of the pool and slide himself in. He loved it and did it over and over from that day. When he was ready. Not when I was ready for him to do it.
3. Start early (if you can). Babies at 6 months old are not afraid of the water. They may be cold (try a Warm Belly Wet Suit, if so), but they aren't afraid. If you start early, and keep the baby exposed to water through the time that they are 2-4 years old when they have the physical coordination to actually start to learn to swim, they will have a much easier time.
4. Do not use floatation devices. They discouraged us from using them in the classes, though, some people did. They theory is that floatation devices give a false sense of confidence and don't really teach children how to swim. Children develop dependence on the devices and don't want to give them up. Let me distinguish between water wings and the full floatation vests. With water wings, the child still has to do some work to stay afloat. We may look into using water wings next summer. There is another theory that the floatation devices give children confidence and allow them to focus on developing the skills, so of course, it is up to you. But we've had so many people come up to us at the pool amazed that Ian isn't wearing a floatation device and he goes underwater without holding his nose so I am inclined to believe that no floatation is the way to go. Of course, you have to hold your child in the pool or stand right by the wall when they are holding onto the wall, but it is worth it. I actually think it is better because it forces you to keep better track of your child.
Taking a swim class with your baby is fun and not that expensive. YMCA's and city rec centers offer very affordable classes. If you can take classes continuously, that is great. If you can't, taking one session of a class will be enough to teach you what to do with your baby to keep baby exposed to water and developing skills.