I'm personally not a fan of notification spam either, but I would assume that notifications via mobile browsers would be opt-in. Is that a bad assumption?
It is not, I haven't seen a browser for which notifications weren't opt in.
In the history of site and app developers so far, yes, a very poor assumption. Assume opt-<whatever drives engagement harder>.
I can't imagine user-hostile features like silently allowing websites to spam you would drive browser share in a wanted direction. That's like expecting people to use your website because you sell their information.