I will try to make a video the next time I see this happen.
Actually, I did reproduce it. And the answer to the question is, it doesn't matter if the video was paused for 30 seconds (or even many minutes).
There is a very brief stutter every time the captions update. It's as if every time the captions update, the video skips one frame.
In most programs, the captions don't upgrade very often, or there is not a lot of motion, so the skip isn't very noticeable.
But if there is, say, panning motion, as there is in many sports, or the captions are updated very frequently - for every word or even seemingly every character as they are being typed by manual caption operators - then it becomes very bad.
I made two videos that showed the stutter / no stutter with and without captions. They are not very good as I was shooting my projector, and handholding my cell phone. They do show the stuttering effect right at the moment the caption lines update, though.
First, without captions :
https://youtu.be/KN66l8Z3ZEoThen, with captions :
https://youtu.be/MchZH0ix_bIYou can see (somewhat) that the scrolling of the genealogy tree is smooth in the first video, but not in the second video, where it stutters each time the caption lines are updated.