Hi Michael, welcome to CrossFit!
The short answer is a resounding "sort of".
Many people combine the WOD with some form of sport-specific training (various kinds of martial arts are the most common).
Others regularly follow a variation of CrossFit known as the "ME Black Box", in which you take the middle day of each 3-day cycle and replace the WOD with a day of heavy lifting (ME stands for "Max Effort"), usually on one of the "big" lifts (squats, deadlift, clean & jerk, snatch). That day's lifting should be fairly heavy and involve at least some maximum efforts (not 3 sets of 8 reps for 9 body parts, more like 5 x 5 on the squat, with as much weight as you can handle).
This variation is popular among folks looking to get stronger, or who have invested a lot in their current size and strength and/or just like the heavy lifting.
But most of us just do the WOD as our primary form of general fitness, and spend any more time available for training either on working specific skills (gymnastics, parkour), or just plain old having fun (i.e., playing).
For those of us doing that, the motto is: If you feel like you could do more than the WOD, you didn't do it hard enough.