It's an interesting thought, and for me, it's kinda true already.
I've given the example of putting my phone in my wife's purse while we go shopping. I do it so I can be more attentive to her and actually participate in the shopping experience. You've seen those husbands and boyfriends trailing behind with their noses in their phones, right? I think the situation is funny, but I wanted to stop doing it.
The watch gives me the chance to remain connected to work or family without also tempting me with brain-rotting distractions. That's why I don't have my phone on my person anymore when I'm with my wife.
So, yes, I spend less time with casual mobile browsing, as it would be called. I also can't imagine casual browsing via the watch -- it's too small, and it's awkward to use for more than quick interactions. I have used mine for skimming news headlines and screening email, but only while sitting down and not for more than a couple minutes.