I found a couple of threads in the past which talked about this. Also apparently another feature is to reduce the impact of a loss to your rival, but I'm not too sure about that because even with a level 1 PR manager, losing to my rival in an away game doesn't seem to impact my attendance much.
If you talk about personal experience, I didn't see a significant drop in attendance when downgrading from a level 6 to level 1 PR manager. That's too small a sample size tho. But then it seems to reflect what I read in the forums.