Depends how much stock we put in Toriyama stating Freeza couldn't surpass Beerus "no matter what he did". I personally wouldn't say God Ki is factored into such, since in-character that was never an option, plus Freeza's potential without God Ki was clearly presented to be leagues above any other character. By how much he already outshines anyone without God Ki, attaining such should allow him to surpass everyone apart from perhaps Zen'o.