IMHO, in a word, no. The ancestors of the Basques probably weren't in Europe when this happened.
America B.C.A fascinating letter I received from a Shoshone Indian who had been traveling in the Basque country of Spain tells of his recognition of Shoshone words over there, including his own name, whose Shoshone meaning proved to match the meaning attached to a similar word by the modern Basques. Unfortunately I mislaid this interesting letter. If the Shoshone scholar who wrote to me should chance to see these words I hope he will forgive me and contact me again. The modern Basque settlers of Idaho may perhaps bring forth a linguist to investigate matters raised in this chapter. /snip [p 173]
by Barry Fell
(1976)
find it in a nearby library
I may not have a chance to dive into the Basque issues until after tax season. Did Barry Fell analyze the ancient Basque writing as he did others from that time and region? I don’t remember if he and Gloria Farley ever looked at that.
I do know that Portuguese sailors were fishing the Grand Banks of Newfoundland very early on. Could Basques also have done so? There is also the report that Mandan Indians apparently knew some Welsh words. Were there also Welsh fishermen in those early centuries. At any rate I wonder if it may be just as likely that Basques and Welsh met up with American Indians on shores not too far from the Grand Banks and left their language traces. I now consider it less likely that American Indians traveled to Europe and left language traces. Perhaps after reading some of the links you have left here and at the other links listed I may have a revised opinion.
The article you posted about which Indians hated which Indians the most not long ago, certainly tells an interesting story about how they progressively pushed or were pushed from East to West over the centuries. Where did the Shoshone and Mandens originate or live 2000 years ago?