_I'm not a fan of throwing an exception from a boolean property._
Not a big fan too but I wanted to do the lesser modification I can. I was pretty sure that someone will raise an eyebrow on that ;)
Now that you mention it, I think that I should convert this property in a virtual method...

_Maybe move this exception into ListRemoteBranches.cs, line 49? Or maybe make an extension method for TfsHelper called AssertBranchSupport(), that checks CanGetBranchInformation and throws this exception?_
Not sure neither of these solutions is a good one... I will try to explain why in your other comment...