In addition to what other have said, I would make sure that whatever arrangement EagleWatch has with the state and federal agencies covers using drones for the observations. Even though Bald Eagles are no longer on the Endangered Species List, they are still protected and harassing them (such as coming in close proximity with a drone) is prohibited.
Also, since this is not a hobby/recreation use for your own personal enjoyment, you likely would need to get a Part 107 certificate to fly a drone for this purpose. Does Audubon have insurance that would cover this?