I think it might. Virtually everyone finds themselves in a "gun-free-zone" from time to time. This ad will appeal to those who have resisted arming themselves for the many reasons that one might resist.
Weapons are expensive. There are downside dangers to weapons. Training is expensive and one never seem to have enough of it. Places to shoot or train can be difficult to find. Safeguarding the weapon and keeping it away from little people and stupid big people is an additional burden.
Every new gun owner faces these and other challenges when deciding to become armed. This ad drives home the idea that even Hillary recognizes that there are risks out there that can only be addressed by armed people at the scene who are ready to act.
If your child attends a gun-free school, if your nephew hangs out at a gay night club, if your son competes in the Boston Marathon, they might be targeted. Those who are ready will fare better than those who are not.
I haven't seen statistics on how many of the numerous guns being bought are by first-time buyers. But I am sure that there are many and we are winning the war against the anti-gunners.