Normal you do exercise 1 finish, exercise 2 finish, and then exercise 3 finish.
But it will be much faster to alternating between the exercises.
Would it make sense to alternating between the exercises in the General Strength and Conditioning II Template?
I personally don’t do much supersetting and go through each exercise one by one. You can superset each pair of exercises on either the 3- or 4-day template. They’re agonist-antagonist pairs in the 4-day template and alternate-peripheral pairs in the 3-day. Either work just fine to do back-to-back, then rest between the supersets. I believe there is some additional commentary in the PDF accompanying the template, but I could be mistaken.
Here is an example:
Normal you do exercise 1 finish and then exercise 2 finish. Like this:
3x3 Squat
3x3 Press
You got 4 min. rest for each working set, so it will be (6*4) 24 min. rest.
But if your alternating between the exercises. Like this:
3 Reps Squat
3 Reps Press
3 Reps Squat
3 Reps Press
3 Reps Squat
3 Reps Press
Then you have 2 min. rest between sets, but a rest on 4 min. between exercises. The rest time will then only be (6*2) 12 min.
Why not always do it like this?
You will get more time for more training or other things in life.
FWIW, in general I’d entertain doing what you suggest if you’re not terribly interested in strength outcomes for the lifts you’re super setting. That’s probably true for you, using the general strength and conditioning templates.
Another reason you wouldn’t want to do this is equipment limitations. You may not have access to two bars and the weights required to complete both.
Yet another reason is that you’re not really hurting for 12 minutes in your day, and you’d rather use that to talk to a friend at the gym or just sit and contemplate your life choices. 
In the first example, yes, I would rest 24 minutes total. In the second example, I would rest 12 min between sets and another 6 minutes (2 min between squat and press) for a total of 18 minutes. I can’t squat and press without 2 racks, I don’t like pressing in knee sleeves, and I want to spend the time training.