As a former radio station engineer, maybe I can shed a little light on this.
The town can't be the entity that permits the cell company to raise the tower, unless the town owns the property. If there is an ordinance relative to such things the town may have the authority to prevent it, but the landowner has to enter into an agreement with the cell company. And it always involves money.
The land is either sold or leased (usually leased) to the cell company for a term of many years. There are many details to consider, such as lease renewal time and terms (more money), etc.
The cell company must do studies on safety (measuring the radiation levels to determine how far the tower can be from a public structure, where the fence has to be, etc). Note: By radiation I'm referring to radio energy - the same type as a regular radio station, TV station, etc. emits; NOT radioactive energy as in nuclear. There is NO such energy from a cell tower.
They also have to make a study of interference with existing radio & TV stations, interference, both radio-related and flight path related to nearby airports, and a few other considerations. All that is very involved, heavily regulated, and expensive - very expensive. One of the things that those studies determine is public safety. When I was still in the business (8 years ago) that was an area that money still could not "buy their way around".
If the school district owns the property, then I would suspect that the parents would have a considerable voice in the matter, to the point of possibly being able to stop it. After, wouldn't the school board have to approve it; and isn't the school board elected?
I can't offer any specific advice, and especially no legal advice, but you may be able to get more info from a local radio or TV station if you have one. Call and ask to speak with the chief engineer or station manager.
Usually when those studies are done, the cell company will investigate a number of alternate sites for a tower. So they may not want to tangle with an angry group who could delay construction. But if the proceedings are well enough along they won't want to stop construction, especially if that is their most desirable site. Remember, they might have a bigger "lawyer budget" than you do.
It all depends on how far along things are, how many people are pro and con on the thing, and things like that. I personally don't like the things either - where I live, I have a view of the night sky that is completely free of man-made light, until they put up a tower down the road - but there are worse things to have to deal with.
I hope I've helped.
Gene Allen
Educational Entertainment Specialist
Elementary School Assembly Programs - Library Summer Reading - Pre-School Assemblies - Gene Allen.