Mostly no. Rarely yes.
Because disabling the ad blocker doesn't just mean hey now ads show up on the page, which might be an annoying audio/visual experience. It means all the tracking scripts behind these ads (and scripts that aren't even tied to displayed ads) now have free reign as I browse this site. Also many ads aren't for actual products or services a normal person might use, but seem to be blatant scams, or lie to you based on your IP/location data. "Mom in [Your Town] Lost 60 Pounds With This One Weird Trick!" That sort of thing.
So it's pretty rare that I say, "Okay, website, I care enough about this content to turn off my ad blocker for you." More often I'll just say screw this and move on. Or use the browser's dev tools to remove the element hiding the underlying content, which is usually more hassle than it's worth.
Also, for folks who are using ad blockers, it'd be good to also block third-party cookies in your browser settings. You'll run into problems occasionally, but if you care about blocking tracking scripts, you probably care about blocking unnecessary cookies as well.
EDIT - As for news sites, I have a paid subscription to one (WaPo), so I can get news there without feeling guilty about blocking ads or trying to get around paywalls.