No, I would more carefully pick and choose which sites I care to visit since I have to pay for them. I can, of course, pick and choose the sites now based on how bad the advertisement is, but because advertisement is so prevalent, I don’t really get a choice because most sites use advertisement. Ironically, the sites I’d be most willing to pay for (like HN) are also the ones with few or no adverts.
The most valuable ones mostly aren't ad supported or paid anyway, and without competition from ad supported sites even more free ones for more purposes would exist and thrive (e.g. if Reddit died all those free volunteer run forums that used to be such a big part of the Web would come back)