Of course the connection is there (maybe because Gosho helped greatly with the research for the movie script and is now recycling the new knowledge of Hyakunin Isshu), though the way this guy was set-up seems too badass/cool for Gosho to just have him be another character for the movie. Plus, he gave himself the localized name of Dr. Watson from the first Japanese translation of A Study in Scarlet before they also used the original names over there (even with the exact same kanji and with claiming to be medical personnel he even has a similar profession) and I really doubt that Gosho would give that to a character that is not relevant to the main plot of the manga but rather a side story that's currently more important for Movie 21.