I researched this several years ago. Here is a page covering both versions of the song by Nasareth and The Everly Brothers. Keep in mind that neither of them wrote it.

http://www.cover-vs-original.com/song-22.html

Here is the results of my digging a long time ago:

Yes. The song was recorded by the Everly Brothers but (possibly even first) it was released as a single by Roy Orbison, however, neither wrote the song. It was written by Boudleaux Bryant (although it was his wife Feline that got him into songwriting). Love Hurts is one of the songs that Boudleaux wrote on his own, although most were worked on by both. Known mostly as songwriters, the couple did perform some of their own songs, especially notable is the Country Music Hall of Fame Vol 1.

What isn't perfectly clear is whether the Everly Brothers recorded Love Hurts before Roy Orbison. Roy released the song as a hit; the Everly Brothers as an album track. Roy's version is dated 1961 (March 1961). A note on an Everly Brothers site states:
Love Hurts [first recorded version] (Boudleaux Bryant) Recorded in Nashville, July 13, 1960 First issued on U.S. Warner Bros. album #WS 1395/U.K. #WS 8028

The "first recorded version" appears to be a reference to the different times the song appeared on Everly Brothers albums, not that it was recorded before Roy Orbison's version. A couple of Everly Brothers sites seem to confirm this. Love Hurts is more universally known as a Roy Orbison song than the Everly Brothers. Many even think the song was written by Roy Orbison; some lyrics websites even give him credit instead of Boudleaux Bryant. Regardless, the known dates seem to indicate that the Everly Brothers recorded it first (in 1960) even if it didn't become as well known or even released until after Roy's. That is understandable given that Boudleaux Bryant presented many of the songs he wrote to the Everly Brothers first.
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I am also a big Everly Brothers (and Roy Orbison) fan so I found this whole history fascinating. Not to mention that I probably had too much time on my hands LOL.