to an old question, I like it!
I think they would be less reliable as ringbearers, but not because they would
fall under the influence of the Ring and want to claim it themselves...
Since the Eagles are (out of choice) removed from the rest of what is going on
in ME (except where Gandalf is concerned), I'd be more afraid of them
forgetting about it, or certainly not guarding it or treating it like it was
important, thus leaving it vulnerable. That's if they agreed to carry it
in the first place, which I don't think would have happened.
Good
question!

Thank you Professor Tolkien!!!!!
"I don't suffer from insanity...I enjoy every minute of it!"