My intuition says, due to the speeds and sizes of the two vehicles and latency of communications there'd be no way to figure out if the interceptor will success

My intuition says, due to the speeds and sizes of the two vehicles and latency of communications there'd be no way to figure out if the interceptor will successfully hit the nuke until it's too late. If the interceptor misses the nuke's location by 50 microseconds it'll explode harmlessly a foot behind it. (The ICBM is probably traveling faster than the shockwave front of the explosive, depending on where it is) I don't think a radar from satellite could be that precise, that fast, and get a signal out.