Personally, it sounds like it is more worry about your daughter than someone being transgender, and given her position emotionally and physically I think you would be hyper analyzing any potential relationship and finding it lacking.
However, this man will have his own issues which he has proactively worked towards resolving, he will have faced ridicule, discrimination and a battle in being accepted for who he is on a level that neither you or our daughter can understand, and to top this off he will have battled with his body image, perhaps gone through some of the same feelings that your daughter will have about disgust and your body not living up to the expectations you have of yourself.
It could be that he is in a really good position to provide a steady example of how you can work through issues and come out the other side.
I had a very good friend in school who struggled with their gender and sexual identity, he later lived his life as a woman, but not as early as this man, I think your daughter may have found a really strong and powerful emotional support in this man...
He could always turn out to be a nobber, but there is not much you can do to stop that happening.
Find out what you can about being transgender, but get involved, meet him, ask appropriate questions when you are both comfortable, and most of all trust your daughter to know what she needs right now.
She sounds like an amazing person by the way, I am sure you are already proud