And if they were named "Welch" wasn't it more likely they were Welsh?
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.