I believe a small number of boys in scouting will continue; especially the ones close to Eagle Scout who have worked hard towards that goal. The real drop off will be in the younger scouts where parents will find alternatives.
Also, as boys get older they tend to drop out of scouting anyway. I suspect parents who would have previously encouraged them to continue will just allow the boys to leave scouting with no protest.
That’s the position my family is in. One son is working on his Eagle project, the other, if he pushes it can be done in a year. I’m Scoutmaster to a newer troop of younger boys and I suspect we’ll wrap it up and join an alternative organization.