No. Johnson is quite old in this photo. I would imagine it was taken in the 1930's and he is pushing 60. The other man is youthful--I would guess in his twenties. Jeffries was three years older than Johnson and would have been quite old in this photo.
I know white people 'all look the same' ... but even so ... that's clearly not Jim Jeffries. I reckon he's probably a fighter though. If so, someone here should know.