Studies have shown that a lack of access to a gun significantly decreases the chances of somebody being killed. So no they won't just grab a knife or strangle somebody.
On a similar but somewhat off topic topic, I find the way some in the MSM and fans have categorizes Belcher's rumored mental illness to be both digusting and horribly ignorant of facts. Being depressed or even dealing with a disorder (ex Bipolar) does not make somebody irrational or even crazy.