DW isn't going to be able to distinguish one case from the other.
And I don't know, I've never tried to illuminate a missile with a STIR before in RL.
The bottom line, is that no one is going to be able to point to a case where a SARH missile from a ship is able to shoot down a missile as small as a SM-2, which is also moving as fast.
Keep in mind, illuminating these missiles is not exactly easy, there is no ESM track, and they're moving at over mach 2...
Cheers,
David