Sort of. The Bugs Bunny we know and love did not fully develop until
Tex Avery's
A Wild Hare (1940) (1940). This Bugs Bunny is an early prototype: he does not yet have the slimmer design or the combination Brooklyn/Bronx accent. This rabbit walks crouched over like
Groucho Marx and has a voice similar to the early Woody Woodpecker, especially when he laughs. (That's no coincidence.
Mel Blanc voiced both the early Woody and this pseudo-Bugs.)
Note that this cartoon was made before--but released a few months after--A Wild Hare (1940).