Simply put the answer is no, you are not required to farm souls. If you understand the game mechanics and decide upon your leveling priorities you should never have to farm for souls to be able to progress.
That is a big "if" though. Leveling a stat you do not need or dying often and not being able to retrieve your souls can put you in a situation where you need to farm to get back on track.
It will mainly come down to how good you are at the game, and how often you die.
(From personal experience, I die far more from falling to my death than actually being killed by an enemy >.<)