^^^^Well not really. I see nothing wrong with doing the HIIT for 20 minutes on the days you do it if you've built up to that. But you really need to give your body some total days of rest on this program in order to keep up the progression for as long as possible, which is the key here.
I love HIIT but it is high intensity and it will impact your recovery. Remember the metabolic demands while not indentical are very similar. You've got to have rest and recovery. Now keep in mind that I am talking about this routine, which is a lot more demanding than people tend to think because of the low volume.
It depends on what your goals are though. If you're focusing on fat burning then it would make sense to do the HIIT sessions on non weight days....just not so many. If I read you right you're doing 4 and you just started, really, with the program. I'd cut it down for now. That is not to say you can't do more but that you should build up to it slowly instead of suddenly overwhelming your body with different demands which will diminish results. And that is even if you have been doing HIIT at this frequency all along, because, remember, you haven't been doing the Starting Strength which changes things.
If your are not focussing primarily on fat loss but are interested in the cardiorespiratory aspect and/or aerobic capacity then you can do it on the weight workout days to great effect. But you need to separate the two by some period of time. I'd want it to be at least 4 hours if not more. I only meant not to do cardio directly after weights. There is a context in which doing both on the same day makes sense you just need to separate them. But of course I agree with focusing on lifting in general
Obviously I'm making assumptions about your goals. Some people want to be "fit" in a cross discipline sort of way, which is great too. But I'm assuming you wouldn't be doing starting strength if that were the case.
BTW, same thing on the stretching before the HIIT sessions. Do it after while your muscles are at their warmest.