WI: Manuel Comnenos marries Constance of Antioch?

[MNP]

He was offered her hand but her mother Alice was tricked and then Constance was married off to Raymond of Poitiers.

What if Alice see through the Patriach's trick and marries off Constance to Manuel? Now, in this TL there's no guarantee that Manuel will become emperor but it's still possible and he'll be an important general for his brothers if they survive or hell he might still become emperor. But what does this mean for Greek influence in Antioch?

[Elfwine]

There's a reasonably good chance of it meaning it becomes part of the Empire again, particularly if Manuel becomes emperor.

Failing that, its certainly tied closely to the Empire, as opposed to how it wasted an undue amount of John II's time and some of Manuel I's.

Since the city is still largely Greek & Orthodox as far as I know, that ought to mean something in these circumstances.