I will speak as an expert on this subject since I have performed hundreds of migratory bird surveys on cell towers and have also obtained several bald eagle nest removal permits from the USFWS. Yes, I am bragging a little bit but it's not often a biologist gets to.

If it is an osprey nest then yes it is late in the season for there to still be flightless young in the nest. It is possible it is an early arrival bald eagle. If that is the case then they can only get on the tower in case of emergency services being interrupted until the eagles have hatched eggs and the young have fledged. In Alabama that will most likely be Late April or early May. I find it odd the entire antenna for the carrier is not working. They do not turn them off because of the presence of a nesting bird. The carrier (ATT) should have a biologist monitoring the site. If its an eagle or osprey, the carrier should be able to request an emergency authorization to work on the tower if the antenna is out and local E911 services are interrupted. USFWS will not grant it just for regular cell service being interrupted.

It's not the strongest species to survive, nor the most intelligent, but the ones most responsive to change. - Charles Darwin