Trouble with firearms boils down to their utterly disproportional power -- a single madman sporting a gun is capable of killing dozens of people before intervening forces can end the spree. A single madman sporting a knife may kill one, two, five, ten others, but not more. Knife-attacks are horrific yet self-limiting.
No, the total will be higher.
From all those cases where right now there is no weapon a weapon, so no incident at least one suddenly becomes available. The number of incidents would go up, but in case of an incident the death toll would go down.
Another post on HN talks about a school district in Texas allowing teachers to carry firearms, but it takes a lot of training in both using the gun and hostile situations. This is a recent thing, so it's still undecided if it will help, but I feel like it helps to have the teachers trained.