I'd expect NYC to say "These vans are strictly for anti-terrorism purposes and if we see a bomb then you're welcome to cite the exclusionary rule from the safety of a non-blown-up courthouse", though that viewpoint will not command a whole lot of support on HN. I think it's probably a loser at the current Supreme Court on a drug case and would get a 9-0 with Scalia writing a florid distinguishing opinion from Kyllo if a terrorism case somehow made it all the way to the Supreme Court. (Amateur analysis here; IANAL.)
You may have stumbled onto a very dangerous idea... not one that could be used for good.
Sort of a funny concept in the day and age that you get no-knock raids where cops shoot your pets with fully automatic assault rifles based off anonymous telephone calls.