Sleek, why didn't he go for the gun before the pepper spray? He didn't say.
Several experts state that the pepper spray has proven much more effective in tests with captive grizzly when you take into account the "effective fire zone". Namely, the spray is far more controllable and covers a larger area than a gun. There is a very low kill rate for people shooting bears at close range in a combat situation.
And again, arguing over what he should have done is just so much armchair ninja posturing until you are in the situation with metabolic residue hitting the rotary atmospheric recirculator at the speed of sound. And ultimately, you have to admit that whatever his actions were, arguably he made ALL THE RIGHT MOVES AT THE RIGHT TIME simply because he survived.
As for whether they will destroy the bear, I kinda doubt they would in this case...my best guess. My line of logic/random thought is this:
1) She was deep in-country, not in a populated area
2) She mauled, but did not kill
3) She acted in a reasonable grizzly-based manner, i.e. defense of cubs. In other words, she didn't start the fight.
