Update: Today was the second class, and Dexter did great. We had to stop at the car wash before class, and that was quite stressful, but no biggie - he calmed down pretty quickly. During puppy play, I made sure to call him back frequently, and he came every time. :-) Overall, I felt that he was much more focused on me. When he started to whine a little, I just walked away from the group, did a quick sit and down and returned, and the whining was history.
I guess, the most important thing is to see what works for you and your dog and what doesn't. I also took his tennis ball to class with me, and during the potty break, we played a little "catch".
If anybody is interested, I had to be a little creative to be able to incorporate ball play while he's on leash. (He's not into the ball on the rope yet at all). I tell him to wait and bounce the ball in front of him a few times while he sits. Then I tell him to catch, and he's allowed to go for the ball once I bounce it. Dexter loves the game, for me it's easy to play while he's on leash, and he has to exhibit some self control and watch the ball bounce until I tell him that's ok. We did have to rename fetch to "go get it", so that he doesn't get confused.
After class, we went to the pet store and he got to snuggle with a maybe 8 year old child. He was so sweet and careful with her, and they were hugging and kissing. Really great day - not complaining for a change.