That's an interesting filter, what type is it ? Llike the model/brand?
And no, I don't think so. Surface agitation can actually be good. The main issue is that the chances your betta making a bubble neset will decrease, so the water moves too much itwould get destroyed. But I have water agitation, yet he stil made it before. And film collects on too-still water if there really is no agitation. I believe this can block the O2 exchange at the water surface.
In terms of stress, I highly doubt it - However, if he is still getting pulled around, you might have to actually do something about the filter.