Sounds like a bit far out for the old P3.
I am sure a P3 would make it easily. When I served as observer on a P3B looking for a yacht in distress off the north of New Zealand, we had about 18 hours of fuel.
If she's 2000 nm out, I guess that's about six hours there, and the same back. That would leave the P3 with more than six hours loiter over the target. And you could stretch that, by feathering two engines, if you were serious.
I am sure the modern engines and props on the P3C are more efficient than the ones we were flying. It would make it easily: the P3 was a very good aircraft :-)