Would it be possible to rapidly induce a Kessler Syndrome to defend against ballistic missile attack?
No. Satellites in orbit are there for months or years, travelling hundreds of thousands to millions of kilometres. It is this time in orbit that provides the opportunity for a
probable collision with orbiting debris; increase the amount of debris and you
decrease the
probable number of orbits before they collide with something, but they will still
probably have travelled tens or hundreds of thousands of kilometres, over weeks or months. But am ICBM doesn't even enter orbit; instead of being in the region of a Kessler belt for years, they streak through in fifteen minutes (even less if it's a continuous boost, low angle arc); the
probability of them colliding with an orbiting piece of debris will be infinitesimal even if you had an enormous amnout of debris in orbit.
Alternatively, could a Kessler Syndrome be confined to a short duration (few weeks or even months) low altitude event that would avoid damaging high altitude satellites?
Debris in low orbit's never going to reach the satellites in GEO; but whether debris remains there for months or years is something you'd have to check with someone with more expertise. Try e-mailing a university astronomy department.