I don't know about "killed it"....
But it certainly didn't help the franchise any. Shadow the Hedgehog was, as I see it, an attempt at expanding the Sonic games into a new direction. It failed horribly at it. Because, let's be honest, in the universe of Sonic, Sonic is the coolest character, and he doesn't care.
Shadow tried to out cool Sonic and well, it backfired. I would say that the horrible Sonic Unleashed, you know, the one where he turns into a Werehog, killed the franchise.
Even by video game logic, and well, Sonic's logic for that matter, that's an outright dumb idea.
I remember renting Shadow from the local video store back in the prominent PS2 days.
I rented it on a Friday because where I am, you could rent games on a Friday for $5 and keep them until Monday.
I took it back the same day because I disliked it so much.
Killed the Sonic franchise? No.
Slipped it the Arsenic? Most definitely.