Not really. To destroy satellite you need suborbital rocket with much lower speed. Usually it is a missile launched from airplane. Even WW2 V2 missile could propably do it, if it had navigation.
Even so, SpaceX can launch 50 satellites in one launch, and each suborbital interceptor can only hit one. And the "if it had navigation" part is doing a lot of work in that sentence; a satellite interceptor kill vehicle is not easy to build. Are 50 of them cheaper than one Falcon 9 launch with a 15x reused booster? I think "maybe" is the only possible answer, but probably the cost of killing all the satellites that way would be around the same order of magnitude as putting them up in the first place. You would need to build multiple whole factories just to make the thousands of interceptors you would need.
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.