Wanted to provide our 3rd solid data point on this:
I had a prequalified offer (not "other cards you might be interested in") on citi's website. No 24-month language, none of the new "one per family"-type language, anything like that. Last plat opened less than a year ago.
Applied using the prequalified link, approved after a painless call ("more information needed"), received letter with 30k/1k confirmation, and have card registered with bonus tracker online.
So online prequalified offers do indeed override the 24-month restrictions, assuming they don't actually have that language in the terms.