In the words of Dr. SM to self, good luck with that boost phase idea.
Neither the S-400 nor the AAD have sufficient response and coverage to tackle what is the initial volley planned in case it does all go hot. Simply the number of launch platforms involved, including decoys and both forward and rear locations make the chances of stopping an attack anywhere in India 20% at best(35% if Israeli David Sling type sensors are acquired).
More laughingly, instead of actually preventing the idea of nuclear war; the BMD has now lowered the threshold where instead of gradual tit for tat escalation, everything goes in one fell swoop since the perception would be that a single launch could be intercepted and then retaliated with a full strike.
Regardless of all the bluster, the stark reality is that Pakistan is 4-5 metropolitan centers as a country and then it is non existent as a state. India has many many more, and not just Pakistan to worry about if the dust eventually does settle; all Pakistan has is India(some would cite Iran but that is a locked up folder in some cabinet near sector G-8 in Islamabad openly every other month for review).