Saor is said as Seer so SEER-la. As in
Saoirse. Not Sayr-la.
I have never come across the name in
Ireland and neither has my husband. I did google and came across an Irish Saorla but then there are plenty of Irish Caitlins(Katelin) these days too.
Also I really can't see any way it could mean noble princess.
http://www.irishdictionary.ie/dictionary