Sadly, there's no such thing as a Rockman Gigamix anime. However, the man and artist himself, Hitoshi Ariga gives us a glimpse into what one could possibly look like. He set it to the Namco x Capcom opening with some stunning results.
Edit: Whoops, my bad. Apparently Ariga-san didn't make this video. He added this in english on his channel:
Thanks to FuPoo and Heatman for drawing my attention to it!