I answered my own question by doing a web search for +"Brendan Gleeson" +fiddle

Of course some of the items I found simply describe Gleeson's part in the film, but yes, the man can play and he got his agent to tell director Minghella that he has this talent as well as being an accomplished actor!

Minghella sent Irish actor Gleeson to study old-time music with T-Bone Burnett. " 'It was wonderful meeting these musicians and hanging out with them,' [Gleeson] said. 'I've been interested in this music for 10 years. I'd listened to a lot of tapes, but I'd never heard it live before.' " (article by Jeff Strickler at http://www.startribune.com/stories/411/4273998.html)