She was certainly shocked when Niall came to her and offered her Whitecloacks troops and didn't react like this was expected as part of her plan. She was angry that Tallanvor and Gill had let Niall come to her and threw a tantrum at first.

Besides, even though Niall is known as a politician, not a fanatic, expecting him to help a Tower trained woman in blatant disregard with the Whitecloack scriptures and customs is quite a leap. But even if that's been overcome somehow, the Whitecloacks would have never accepted Elayne - an actual channeller, trained by Aes Sedai, and strong enough to make Accepted in less than an year, as a heir of the Lion Throne. So If Morgase intended to preserve Elayne's claim, getting the Whitecloacks backing was a terrible idea.