No there is no link. Actually I would expect Neolithic Western Europeans to have had darker pigmentation than present-day Western Europeans. Neolithic populations originated in the Middle East and North Africa. R1b originated in Central Asia before passing through the Middle East to the Pontic Steppe, where R1b men mixed extensively with blond and blue-eyed Northeast European women. I would think that the Indo-Europeans introduced blue eyes, fair hair and red hair to Europe, or at least re-introduced them where they had been overridden by Neolithic immigrants.
The Black Irish just inherited more Neolithic phenotypes than other Northern Europeans. That is because they were the furthest from the source of the Indo-European migration (along with Iberians) and therefore inherited the most diluted autosomal DNA with their R1b. R1b remained unchanged all the way from the steppes to the Atlantic fringe of Europe, but their appearance became increasingly similar to the local population they conquered as they interbred with local women. Besides, England and Scotland got a fairly recent introgression of fair pigmentation from Anglo-Saxon and Viking migrations, which, in Ireland was mostly limited to coastal areas, especially in the Pale and in eastern Ulster.
I imagine the Neolithic inhabitants of Britain and Ireland as having straight black hair and being both long-faced and long-headed, like modern north-west Iberians. This kind of phenotype reminds me of
Christopher Lee (Saruman in Lords of the Ring), who could easily pass for an Castilian or Leonese.