My initial plan was to do the pool and classroom work at home, and the dives in Maui, where my in-laws live. I didn't end up doing that, and I'm very glad I didn't. Here's why: Diving, in my experience, has a lot in common with skiing. If you watch someone who is good at it, it looks like a blast. But when you're starting out, you don't carve beautiful S-turns down the mountain -- you snowplow, and it's awkward and way more work than you thought it would be, and not nearly as much fun. And the only way to get out of the snowplow phase is to ski more (and maybe take some more lessons) until you get to where things start to be graceful and elegant and . . . well, FUN.
Diving's like that. When you're learning, it's all about process -- how do I manage my buoyancy? Where's my buddy? How does all this equipment WORK? It takes time in the water to become relaxed and facile with the equipment and the skills, and only then do you really have the bandwidth to take in everything that's around you. If you only dive in the tropics, you are unlikely to dive often, or to get enough bottom time to learn to become one with the water. Diving at home, although it may not have the appeal of clear, water water, is where you can learn the joy of weightlessness and freedom in three dimensions, which is one of the most utterly addicting things about the sport.
My advice is to take your class at home, go to Cozumel and enjoy the dives there for fun, and come home and continue to dive locally. It's worth it.