Groucho is an insulter, a quick wit, and I don't see how, in that particular role, he could have been able to do that. Sure, there are a few times when Milton Berle gets picked on, but you could have everyone referring to Groucho as "Old Bag".
What I don't like about that movie, is the fact that it shows how Hollywood has changed.
You could not do that movie nowadays.
There is no actor in Hollywood that could do the Spencer Tracy role the way he did.
There is no comedy troupe that you could put in the Stooges place to get that same "Oh no!" type reaction.
If there was an effort to remake that movie 100%, there is only one role that I see being filled where the actors are even close:
Jerry Lewis -> Jim Carrey