That seems optimistic in any sort of realistic scenario. The everything works perfectly and there’s one ICBM and nobody modifies anything as we start launching all this stuff into orbit, then maybe.
How many satellites do you need to reach that kind of coverage? And how many interceptors per satellite to hit everything from one or more nuclear subs launching from the same location near a major city. How long does it take you to react without risking false positives making the system useless etc.
The problem just gets ugly fast.