Yes, it's a bit unlikely of a way for him to be remembered, since singing wasn't his strength, what with being a comedian (and a unique one at that), although for his gravelly voice, he had an impactful way of delivering a lyric.
One of the song he was know for was "September Song," written by Kurt Weill and the playwright Maxwell Anderson for the Broadway show Knickerbocker Holiday. And happily, we have a video of it from a TV broadcast in 1955.
Durante has a very long career, taking him into color television. So, as a bonus, here he is with the same song in 1972. One of the things about Jimmy Durante is that he seems to have been born looking like an old man. So, he could sing this for a long time. Even in his movies in the 1940s, he doesn't look all that much different than here. (His movie debut was back in 1930 -- and I wouldn't make a bet that he couldn't have sung "September Song" then, as well.)