It's an interesting idea. They are deployed and start spreading out within minutes of launch. You might be able to take them all out in the first couple of orbits. I expect it would be much harder after that. SpaceX could possibly defend against this by varying the orbit so you don't know where to place your interceptors, and maybe by having the satellites boost apart from each other sooner.

But you'd also need to take out most of the on-orbit satellites before it would be useful to blow up the replacements.