No. As Perl mentioned, Character Transfers weren’t a thing in Vanilla, so neither are they available now. I know of no plans to include them.
Edit: Since this statement has received a bit of criticism I wanted to correct it. I misspoke when I said that PCT’s weren’t a thing in Vanilla. They were, they were introduced late into “vanilla”, mid-2006 as far as I can recall, which I believe is just before patch 1.12 that we’re modeling for Classic.
As for them being in Classic, as it stands the option is not currently available. Will it be? It is entirely possible. John Hight said “It is something we might want to support”, that isn’t “something we will support” or “something that we will have”. Until there is official world that something will happen we’d be unable to state it as a certainty.
There are better ways to express yourself, folks, please keep that in mind in the future.