Yes, the Eagles would have been greater in those days but they could probably challenge Smaug if they fought together.
I don't think Smaug's fire would have been hot enough to destroy the One Ring (if any Dragon's fire ever could have).
Was the initial post asking what would have happened at the Black Gate? If so, more Eagles would have died (possibly) but it would have had no effect on Frodo's quest. Unless Sauron convinced Smaug to guard Mount Doom. That could be an idea.
