I really don't think the sign has anything to do with it. It's easy to reason that an elementary school is going to be filled with mostly children and some adults who are not that likely to be armed anyway. Not having the sign isn't going to change anything.
But let's think it through, imagine we raised taxes to get enough money to have an armed guard in every school full time. The target has not be hardened a little. What about all the other soft targets? Should every business have a full time armed guard? Every playground? Every library, etc.? If a shooter really gets scared away from schools because they now have armed guard then they will just pick another target. Therefore for this proposal to truly be effective we are talking about armed guards everywhere and all the costs that are associated with that including increased taxes and the price of goods.
Furthermore this has actually been studied. There have been armed officer in schools for years yet little to no evidence to show that they actually prevented school shootings. There were one or two instances where an armed guard stopped an active shooter but not enough to show statistical significance.
Look at all the tax money over the decades of years we have paid to "protect" our politicians and the POTUS. How many times have all these paid security people actually stopped a killer from killing these people?
I would say not enough to justify the total expenses. But still, we do it. Why? Because these people are that important?
What degree of importance do we place on these children and school personnel to be even thinking of the expense of armed security because the cost might be prohibitive?
We spare no expense when it comes to protecting these "important" people but haggle about costs when it comes to protect our children and workers in schools.
The politicians who are harking about more gun control measures yet maintain their security personnel are hypocrites.
edited to add: And yes, the sign has nothing to do with it. It will not change anything. I mentioned it to highlight the sheer insanity of it all. The only thing I agree with you on.