My male cousin is a direct descendant of our Scottish McConnell ancestor. He is an R1b-L21 descendent.

Information I've read is that Ulster-Scot McConnells emigrated from Scotland to Ireland during difficult times:

England Under The Tutors p.305
https://books.google.com/books?id=blKgAAAAMAAJ&pg=PA305&...

Now in Antrim there was a considerable colony of Scots from the Islands, whose chief was James M'Connell. Also, a sister of the Earl of Argyle, curiously referred to in the records as the Countess of Argyle, was the wife of O'Donnell. The Antrim Scots were supposed to be in alliance with O'Donnell; whom however Shan's proceedings were now causing to seek English friendship, whereas the Scots were antagonistic to Elizabeth, holding that their own Queen Mary had the better title to the English throne. So Shan got rid of his O'Donnell wife, and married the sister of James M'Connell by way of cementing a union with the Scots; but then proceeded to write to Argyle, suggesting that he should get rid of the M'Connell wife in turn, and that the Countess should be transferred from O'Donnell to himself, on the assumption that this would give him an equal hold on the Antrim Scots. Whereby he merely enranged the Scots and disgusted Argyle. However, a short time afterwards, Shan raided Tyrconnel's country, and carried off the chief and his wife; who seems to have been fascinated by her captor, and willingly became his consort, irregular as the conditions were. M'Connell was somehow outwardly pacified despite the insult to his sister; but the bad blood engendered took effect in due time.

Another article which might tie Irish & Scottish M'Connells:

LINK: http://www.archive.org/details/factstraditionscOOmcco
LAURISTON CASTLE LIBRARY
FACTS AND TRADITIONS COLLECTED FOR FAMILY
EDINBURGH: PRINTED BY BALLANTYNE AND COMPANY.
M.DCCC.LXI.
Digitized by the Internet Archive in 2012 with funding from National Library of Scotland