Working from 30+ years memory, the answer to your question is probably a definite NO; the warhead explodes. While there a few different warheads out there, I would think, to get better odds, that a continuos rod warhead was used. I don’t recall any specs, but the rod expanded vs fragmented, and any aircraft struck would start loosing pieces of airframe.
While the SM-3 is certainly more advanced than the below diagrammed
RIM-66, I would venture the layout is similar and utilizes one of various explosive devices to do the intended job.
The pointy end contained the TDD(Target Detection Device), which is way more advanced now, followed by an electronic homing radar or the warhead.
The old ones were guided by director radar from the ship. I’m pretty sure the new ones are homing in the terminal phase of flight with shipboard radars mainly just giving it good advice.
The RIM-67 was basically a RIM-66 with a booster attached. Impressive when fired. Lots of noise and smoke. AAAAARRRRGGGGHHHH!