No, “welsh” or “welsch” and its variants is simply ancient Germanic for “stranger” or “foreigner.” To the Anglo-Saxon invaders (illegal immigrants, one might say), the original Britons (well, I suppose they illegally invaded too, but in pre-historic times—the Anglo-Saxon invasion is better-recorded) were the “furriners,” the goofs, the strangers, the weirdos.
Welsh, Irish, Scots, Bretons — all Celts, all pushed into the hills and scrublands, all Welch/Welsh/Welsch.
Thanks, Houghton! Very interesting. You are truly worthy of your screen name.