Only the SM-3 can intercept a ballistic missile, and the intercept point MUST BE OUTSIDE THE ATMOSPHERE (the actual seeker and final stage are not aerodynamic.)
The problem is, fired near the launch point, an SM-3 Block I can't catch up to a ballistic missile in a tail chase; it's too small and too slow.
Unless the missile launches fail, everyone is just going to be waving at them as they go by, even if they are launched over Japan.
Boost phase intercept only would work with a ginormous missile - one was under development (the KEI) but it was canceled. It wouldn't have fit on a US Navy surface ship.
I’m not so sure that an SM2 couldn’t perform an intercept from short range when it has the missile rising off of the pad. A rocket of that size has to accelerate up to speed, while the SM2 has a much faster rate of acceleration.
From 15nm, the rising ICBM might not have even attained Mach 2 yet at time of intercept. Remember that modern intercepts don’t fly a rainbow trajectory.
But it would absolutely depend on the ICBM’s rate of acceleration and when it performed its tip.