Would be better to intercept later in flight
The trajectory of an ICBM becomes largely fixed a short time into the flight after the boosters burn out. At this point, leaving terminal warhead guidance systems aside, the path can be predicted.
If the missile was flying over, or at U.S. territory, we could probably legitimately shoot it down (assuming our shoot-down system works yet).
It might be bad precedent--I haven't thought it through all the way yet--to shoot a test missile down that was heading along a harmless route. Nuclear missiles have been tested like this all the time, and as far as I know, the tests were not considered acts of war. Political belligerence, yes.