I have to say, that's one romance that they can just do away with entirely. I could never buy it in the books, since we never got to see anything about it until we saw that letter.
Ah sorry, I might've misinterpreted - I thought the comment I replied to was about whether a normal, non-Oath Rod...
If she swore under the Light and hope of salvation and rebirth, she wouldn't break it regardless of Aes Sedai - nobody would. I don't think Aes Sedai are forced to hold to their promises though, however she could obviously not say it unless she meant it. Make a promise that you intend to keep...