Given what we know of spree shooters around the world and in the US, they strike me as predominantly desperate, mentally ill people. We had the Columbine shooters who seemed to be more vengeful than fame-seeking. We had the Aurora shooter who didn't do any grandstanding when apprehended, or in fact talk to the media at all. And of course, we had the Newtown shooter who didn't leave behind any notes, manifestos, or in fact any evidence that he wanted to be infamous (even if posthumously).
These don't strike me as people who are driven by the ensuing media coverage.
Don't get me wrong - I've been appalled by the news media surrounding the Newtown shooting, particularly CNN's journalistically abhorrent fingering of an innocent individual, but I don't think the coverage is really the crux of it, and I don't think taking it away will stop them.