D&D bards were created by Doug Schwegman in Strategic Review Vol. II, Issue 1, which came out in 1976 during the OD&D era. Bards were adopted and adapted by Gygax in the 1e PH but they did not originate with him.
Sure. But...
A) That's at least three years of Bards being a thing in D&D prior to Appendix N getting written.
B) Anderson and Wellman are both clearly among authors Gygax loved, and those stories were no-doubt well known. I can't document at the moment for certain that Gygax read them, but I'd be surprised if he hadn't.
Even though Gygax didn't come up with the original concept of bards in D&D, he did adopt and flesh them out, and Cappen Varra, Silver John, and Kardios seem like
the three major D&D-style swords & sorcery (well, spooky folklore adventure, for SJ) protagonist bards.
Fflewddur Fflam from Prydain predates D&D, but is a bit more tragicomic sidekick (though he implies the existence of and speaks of more serious and powerful bards in the setting).
Gygax does make a point by the 1e PH Bard of trying to tie the class in somewhat to historical (or quasi-historic, with the Welsh Eisteddfod harking back to 12th century practice, but the 18th century revival being full of dubious scholarship and inspired in part by outright frauds like Edward "Iolo Morganwg" Williams) Celtic bards or poets. It's a little ironic that Gary went to Irish for a lot of the nomenclature of the bardic colleges and instruments, given that in ancient Ireland musicians were actually lower class, compared to the exalted
Filídh, who were poets, genealogists, historians, lorekeepers, and magical prophets (practicing
Imbas) in service to kings.
My theory may be wrong, but it really seems weird to me that Gygax could be such a fan of Anderson and Wellman but NOT be influenced by their bard characters in writing the AD&D one. Especially since they're roguish, clever warriors, but also know some magical lore, which again corresponds closely.