Eagles are servants of Manwe, and thus thought of as similar to Maiar in spirit. This would mean they have souls or 'spirits' so it's presumed that they would be affected by the Ring just as Gandalf or Saruman would be.
The dragon possibility is kind of moot since there were none left (at least that would prove to be a threat) after Smaug went down. I doubt Smaug would've used it - he didn't seem disturbed when Bilbo came in with it, so he was probably unaware of its power. Smaug wouldn't have found it in all his riches.
__________________
...take counsel with thyself, and remember who and what thou art.
|