I love this sword:

http://www.christianfletcher.com/Site/Irish%20Ring%20Hilt.html

But I'm curious about its historical authenticity. Were there--or could there theoretically have been--period swords with this kind of hilt on this kind of blade?

From the originals I've seen pictures of, no. Many have characteristics to the Type XIX family of blades. Almost all blades of Ireland when the ringhilt was contemporary would have been imported continental blades. This hilt type seemingly appeared at some point in the mid to late 1400's. I've never seen one earlier than that. An irish Type X would have a norse hilt or an Irish interpretation of a Norse hilt. Maybe some brazil nut pommels for later periods, especially after the Norman invasion. The mating of these two is somewhat of an anachronism I would think.