Before I get to the reasons I will just say without even giving this any thought whatsoever it sounded like a bad idea. Sure there might be some CSS that is incompatible across browsers but those situations are definitely a minority. Remember CSS is a standard. So the majority of it is going to be implemented across the board.
But for the more logical reasons:
Performance would be a major issue to consider as now your clients browsers are going to have a lot more to process. Plus js is linear so everything would have to wait for the prior function to finish, there are some workarounds to this, but for the most part this could be a big issue.
What you can accomplish in a few lines of css could be several more with js. And that would be per page since you couldn't really reuse a lot of it.
What happens when you leave your place and a new developer comes in and wants to change styles across all pages. Guess what he's screwed?
I can't even seeing this saving you anytime because with css you can write in one place and apply everywhere. With your js solution you would have exponentially more code to maintain.
The other reason you mentioned with js turned off. Sure your ajax calls aren't going to work like you mentioned so there will be some problems but at least they will be able to see what your site looks like without just seeing a bunch of text everywhere.
I could go on but I think you get the point this is not a good idea by any means.
Of course, this is just my opinion so take it for whatever it is worth. But I think you would seriously regret this decision.
EDIT: Sorry for the novel. One last thing though, the article you referenced was about CSS selectors and not overall css.