No but if あなた go to his ファン club site which is David Tennant dot com または something like that they have an address あなた can use to write to him but remember he is very busy and it can be some time before あなた hear anything but if あなた enclose SAE he will sign a pic for あなた and he tends to put your name on it:-)
I'm new to this site, but I'm fairly sure that it's only a ファン site, and I know for a fact that David does not talk to ファン on the internet, so I don't think あなた can. I'm sorry to tell you. I would be in HEAVEN if I could! Haha :D
