That's a good question. I did research with N15-enriched fertilizer (isotope tracer). The fertilizer was applied early in the season. Later, I took samples of leaves, soil and crop and had them analyzed for N15, to see where it went. Yes, the trees did take it up, indicating that they absorbed N from the crop field.
In this type of experiment, it's important to do trenching in some of the plots (as a control) - dig a trench between trees and crops and line the trench with black plastic underground, to prevent tree/crop roots from interacting.
There are several models nowadays, including Wanlucas and others.