Nah, I think the eagles would have been too conspicuous. I don’t see how they could have made it to Mount Doom, while Sauron’s power was still strong. The ring (and Sauron) needed to be destroyed first before the eagles could fly freely through Mordor. The evil forces under Sauron never would have let them get to Mount Doom alive. The Nazguls’ creatures could fly too after all. The hobbits and Gollum made it because they were small and could remain mostly hidden or disguised.
No course is without risk.
But I think an eagle strategy would’ve had a far greater a priori chance of success than what was actually followed.