STM on a 5D3

I occasionally use my 5D3 for video and, once or twice, tried to refocus while taking a video by using the AF button. Once or twice was enough because of both the noise that the 5D3/24-105 combination makes when refocusing and the lack of smoothness during the refocusing period. I either have to remove that secion from the video or live with the transition in the videos.

I have been wondering if the 40mm STM lens, which I understand was designed for video refocusing, would work decently on a camera like the 5D3. Has anyone tried this?

And, if so, is the 5D3/40mm STM quieter during refocusing than a "normal" lens? And is the refocusing "smoother"? Or does the STM lens only work properly with a camera designed for it like the t4i?

I would prefer to know before buying the lens. It is not expensive but US $150 is still $150 and, if the lens does not work quietly and smoothly enough on a 5D3 to take videos with, then I should use the money for something else instead. Any help would be appreciated.

Thanks.