Only in the sense that they popularized the genre, but I find it hard to believe that they were in any sense the first college rock band.
Musically, The Feelies were doing everything R.E.M. did on Chronic Town two years prior. They had the jangly guitars, the pounding rhythm section, the murabled vocals complemented by distant harmonies, and most of all, the devoted college student following. Not to mention that Radio Free Europe is basically a Feelies rip-off, even though it's a fantastic song.