Followed correctly and with a good mass oriented eating plan, 20 rep squats will definitely help beef the legs up, thats for damn sure. The big thing with that program is that you have to be doing a legit "20 rep squat" and not a "I can squat this weight 20 times" kind of thing.
Its a weight you could honestly only do 10 times if you did it as a single set, and you keep the weight on your back after rep number 10... Breath for a few reps and hit another 2-3 reps. Breath deep 3-4 times, hit another 1-2 reps, and so on until you are at 20.
These are absolutely brutal, if you arent seriously questioning whether or not you can get 2 or 3 more reps you arent doing it right.