Not always. I've removed gut hooks that have caused massive bleeding and tearing, only to have them die soon after, as I find them floating shallow. Then I caught some with gut hooks, fully alive and healthy. Stopped removing gnarly gut hooks like the kind that killed fish. Can't really say, but when I've caught fat gut hooked fish, and when I don't see floaters in small ponds after gut hooking fish, I'd say in some cases leaving the hook prevents death.
Key words being gnarly and sometimes.