The rumour mill works both ways, I would imagine. If both Sir Walter and Mr. Elliot frequent places like Tattersal's and the House of Commons, I would think those places are both rife with gossip of all kinds.

If Mr. Elliot had been determined to make a 'mercenary' marriage, as it seems he was, he could probably have easily determined that Sir Walter's daughter was not worth pursuing in a financial sense. For all the show they put on, I doubt that the financial situation of Kellynch hall was really that much of a secret. That, plus the off-putting manners of Sir Walter and Elizabeth would have been enough to keep him away. For a man looking for a fortune, it's one thing to marry a woman you don't care much about, or even dislike (as Willoughby did in S&S), but it's out of the question if there is no financial inducement.