It is always early to allow for the lessons before the park opens. The class size is very small and personal with lots of waves. It is one of my DD's absolute favorite things to do. Yes, it is exhausting. You carry your own board back up the hill/walkway to start all over again. I would not advise it for anyone not used to vigorous physical exercise.
I cannot comment on transportation as we always rent a car and just drive ourselves there. I would imagine that you would have to pre- arrange a cab otherwise as I cannot imagine Disney providing transportation.
If it is something you or your kids enjoy it is highly worth getting up early to do. You can either spend the rest of the day in the waterpark (as long as you have a entry ticket as lessons do not count for entry to the waterpark) or we usually just do a resort/pool day for the rest of the day and maybe evening entertainment and dinner at one of the parks.