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Probably not. Depends on the trajectory the NKs fire it on and therefore its altitude when crossing over Japanese territory. It is likely however to be too high (?) for the SM-3 Blk 1As to reach. The Patriots are (as someone else pointed out) endo-atmospheric terminal defense systems.

That said, it is still a good idea to deploy and make ready the missile defense assets. This is after all, NK rocket technology. There is a significant probability of a malfunction and the vehicle and payload (whatever it is) could fall way short. Being able to engage it and at least detonate/destroy the volatiles/fuel on board could reduce the risk to anyone under its footprint. Besides, even if they don't engage it, just having the sensors (radars, IR?) and crews on station and tracking it will provide valuable intel and training.

Okay...anything in the AO that CAN shoot it down?

If the missile was fired at Alaska, the GBIs based in silos there would have a shot at it (as it approached Alaska, not over Japan) The GBI has barely been tested under real-life conditions, but it is physically capable of the interception.

The issue isn't mostly the range of the trajectory, it's the acceleration and geometry of interception in boost or early mid-course. You need a truly enormous, very fast,very expensive missile - which the long-canceled Kinetic Energy Interceptor was.

The Aegis SM-3 Block II which has an IOC of 2018 has a shot at ICBMs in early midcourse. It will be the first missile so big it completely fills a strike-length VLS cell top to bottom, side to side - SM-3 can't get bigger after that without new ships/new VLS.

So until 2018 the Japanese can't do jack squat about any ICBMs flying over Japan.

The Japanese PAC-3s already exist so it isn't a big deal to "deploy" them. And any statements about them probably refer to intercepting a failed ICBM (which is a high probability) that happens to fall towards Japan.

All of this is basic physics known to all/open-source/unclassified, btw.