Thanks for your enquery! There is a slim possiblility that there could be a connection. However, since you state that your ancestor James Pyne came to Massachusetts in the mid-1800's, it is unlikely. Those emigrants were most likely a part of the great Irish Famine migration to America, Canada, and Australia. They came in 1848-1855. Most of them were from the western Counties of Ireland.
Cork is the larest County in Ireland. So, unless you can tell be just where Balty_____ is located, I may not be of much help. Also, tell me what their religious leanings were. That made quite a difference at that period. If they were, as I gues, Roman Catholic, there might be some Parish Records still to be found in Ireland. If, however, they wer "Church of Ireland" [ie, Anglican], a very great deal of those Parish records were destroyed in the disastrious fire at the Four Courts Building in Dublin in 1922 and are lost.
The family data I have comes mostly from the north eartern part of County Cork - near Fermoy. A place called Kilworth. There is a good bit of data onthese Pynes, found in "The Irish Genealogist".