Well of course it's (usually) going to be a small factor over the long haul, but as you said yourself - small factors can have dramatic impacts.
Sure. In small samples. The issue here isn't so much that lineup protection is a "small factor," it's that the larger the data the smaller it gets. When you have as much data as we have for baseball and people
still don't find anything statistically significant about protection--and to put in perspective how unlikely that is if there really is lineup protection, keep in mind that they
have found things like a .1% difference in strikeout rate between ballparks statistically significant--then odds are it just plain doesn't exist. If it does, it has an overall impact of less than one run per season.
I guess we'll have an interesting side experiment to watch if Dunn leaves 
The only reason I can think of that Zimm might walk less with Dunn out of the lineup would be if he felt like he had to get the "big hits" and swing for the fences to compensate, which is something that any competent modern hitting coach should disabuse him of. But the lineup overall will definitely be a lot worse without Dunn.