Well, it seems Mr. Elliot is a dashing wooer ;-). While Mrs. Clay might have been desperate, JA does tell us that her affections overcame her interests. But what were Mrs. Clay's prospects of second marriage? It does seem that Mr. Elliot is responsible for her once she is established under his protection and she is also a liability to him. Even if he wants to marry again to somebody other than Mrs. Clay, she could contact this future bride and ruin his chances if the bride is scrupulous (like Anne, or Anne's mother).
Another thing you made me consider is how Lydia's actions were taken less seriously than Maria's (Mansfield Park), because Maria was married. So what about a widow like Mrs. Clay? I think it is more like Lydia's case, i.e. her honor can be redeemed by marriage.