When in sport mode the AC will not be as stable and the video might be jerky but there is no reason you cannot shoot video at high speeds, there are numerous Youtube videos out there shot in sport mode at maximum speed. Here is a link to one on the DJI site: How to: Fly the DJI Phantom 4 at High Speed - Sports Mode
You can shoot in sport, but not much point as the video will be poor.
I use Premiere for post production and very easy to speed up sections of the video to give a much better result.
The primary problem is the props will be in the video when you accelerate fast in S mode. You also have no obstacle avoidance in S mode, a little insurance that's nice to have when focusing more on capturing video.
In Sports mode I find most important to adjust the Yaw. I lowered it to 0.20.
(Switch remote to "S" while being in the Expo settings)
Before that I wasn't able to keep a constant direction. It was too sensitiv.