Among diehard boxing scholars? Yes. Nobody can have fought six times with SRR and not be famous in this niche. Among casuals, though, who knows...
Of course not. Boxing geeks, researchers and historians would have always known about him, but even a good portion of them wouldn't rate him so fondly had it not been for the movie. As too the boxing/sporting public, leaving aside SRR and Jake, just ask them how many great middleweights and/or fights can they name and tell a little about? the answer would be very, very few, and you could make it easier yet and ask them to name any great fighters, any weight in general pre 1960 and comparatively speaking it would still be very, very few. Movies, Books and Documentaries restore the names of athletes in ALL Sports and dead sports like boxing sometimes still need even more help than them.
He still had the book which was a best seller and prompted the movie so probably close. Obviously, the movie would have reached more people but je would have still had a big following.
OP did specify "with the boxing fans", however. Sans the feature biopic LaMotta would be less famous amongst randos on the street but that isn't strictly what got asked here.
Lamotta still probably wouldn't have been as popular because, at least for me, people got introduced to him through the movie. I didn't start reading the book until 2 weeks ago. I watched the movie for the first time 5 years ago.
