It'll be very effective in producing a warm fuzzy feeling in the gun hater crowd. They usually rely on emotion instead of facts so it doesn't matter if it actually changes anything. As long as the gun-grabbers can say they tried their conscious will be clear. That's all that matters to them.
If the Obama administration really cared about protecting children at schools it would call a meeting with administrators, parents, security experts, firearms experts, and mental health professionals. Guns aren't the only issue.
Here's something to ponder. If the shooter had blown up the school would Obama start talking tough about explosives?
In short, no it won't. The policy can contain all the good will and thoughts and while the concept behind the policy is fine, carrying it out will be difficult to impossible. It is simply unrealistic to expect anything on a large scale from such an unwieldy body like the government, not even to mention the practicality of the policy itself.
I'm not sure what effective really means. This is not something the public really cares about, and this issue will quickly fade as it always does. Biden is not serious about this; it is political gesturing as it always is with this Administration. It will will quickly fade as something else becomes news, as it already, frankly, has.
People who don't understand history sometimes read the Second Amendment and misinterpret it as being stronger protection than it is for guns. While some regulation may help, it is a change of culture that is needed. Folks need to be less paranoid about their surroundings and not glorify guns as a solution to danger.