I looked at the program and it looks sound. You do the initial test to find out an appropriate place for you to start, and then progressively add more reps. You have rest days and you're NOT encouraged to "go for the burn" in which case you're likely tearing muscle fibers and are going to be rather sore. The soreness from a "no pain, no gain" attitude early on is going to throw you off schedule and likely lead to drop out. I think if you push yourself but not too hard at first (as they suggest in the program), to give your muscles and tendons a chance to adapt to the new stress of doing push up's, you can start pushing harder later once your body is more accustomed to the exercise. Don't be discouraged if you take longer than the 6 weeks in this program.

Good luck!