Who would have ever guessed we'd be this spoiled for choice in playing original style D&D. I just grabbed the dice, the screen, and the hardcover; maybe I can bring the additional classes over to Delving Deeper.
You should have no problems at all doing that. S&W: Complete mimics how many OD&D campaigns progressed as the AD&D books were released BitD. IMO it is a good mix of the speed of play and simple mechanics of OD&D with the greater variety of options of AD&D.
As an added bonus, my son's group in a nearby town play S&W:C and I get to play with his group when I go visiting.