Absolutely. I have seen a number of articles about such families, and always there was a strong, obvious role - usually by a pushy mother - who very much wanted the special status of having a transgender child. They were very invested in the role, and full of talk about their pains in facing up to a homophobic world.
There is a lot of information about trans regret at the following website. The author did an analysis of an interview with "transgender" boy and his mother, and pointed out how she was good at steering him into the conversation she wanted - I can't find the link to that exact story, but the site in general is here:
http://www.sexchangeregret.com/wwwsexchangeregretcom
My daughter met one of those kids in the hospital. It struck me as an extreme form of Manchausen-by-Proxy on the part of the parents—and utterly sick that they found a doctor to go along with mutilating a minor. And I’m sure they all wondered why the kid was in and out of the psych ward on a regular basis.