They, the AN/SPY-1 has the ability to track exo-atmospheric targets at very long ranges. Let's just put it that way. Their vertical scan range exceeds their lateral range, this is due partially to Earth's curvature, diagonal vertical distances being longer than horizontal distances over a curve. Even our AN/SPY-1F has a scan range in excess of its stated perimeters. Depending on the baseline, you can have scan ranges exceeding public info, each baseline offers not only software, but hardware upgrades as well. Each upgrade rectifies some fidelity problems with weak signal return from long-distance tracks.
Scan range is a function of "where" too. With higher altitudes yielding greater scan distances. Aegis Ashore, and its sea-based counterpart, will and do have the capacity to track and engage ultra-long range targets. Though as I've noted previously, in past posts, this is a system that works in conjunction with other sensors. No system relies on itself alone. They are networked.
Aegis can engage ICBMs once SM-3 Block IIA enters sea-based operational capability. At present with the shorter ranged SM-3 IA and IB, no it can not.
That doesn’t mean tying Aegis BMD ships down on coastal patrols, Cooper emphasized. “I have never bought into the idea that Aegis should be assigned a ‘picket ship’ role, which the Navy would rightly oppose,” he told me, “but the ships normally near our coasts have the inherent capability to shoot down ICBMs from Iran” — or a sneak attack from a ship offshore.
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This aside and moving onto another aspect of this discussion, since SM-3 isn't using AN/SPY-1 alone and since this discussion is about Turkish SM-3 prospects, one other system that would be needed to work in concert with AN/SPY-1 is
TPY-2, which has a scan range in excess of 1000km. This radar is better known for its role as part of THAAD:
The tests include ICBMs, one of which is the Trident C4:
It is typically configured in an MRBM role, but features an extended range configuration as well.