It depends... if you're shooting a 177 grain round, patched rifle ball at a deer at relatively short range, that will most certainly do the job even though you won't have as great a muzzle velocity as you'd have if using the .45/70/350.
And... you definitely won't have as great a retained, down-range velocity with your Hawken compared to a .45/70's much heavier bullet due to the shape & weight difference of the two projectiles... round ball vs. pointed, lead bullet... because of the .45/70's greater muzzle velocity plus it's better, retained, down-range bullet velocity.
However, in spite of these differences, even a big buck deer probably won't know the "difference" if you place your shot where it should be.
However, if your game is a 2,000 pound male bison or a 1200 pound bull moose... you may have a bit of a problem if you're using the Hawken.
Jus' my 2�...
Strength & Honor...
Ron T.