Well, why not? I have never had problems doing that with my favourite singers. Even now I wouldn't have problems writing an e-mail to Matt full of hearts since I shout his name everytime I see him on concerts (you have found a Matt fanatic). Anyway, you are a fan and, for what I know, singers are always happy to have many fans who love them, so, yes, you can show him your portrait to let him know that you care about him!
Hmm, ok, maybe he isn't the administrator of that page. I think that the real Matt writes only on Twitter, sorry I checked and there aren't even e-mails on Muse official site! At this point you can just wait for a miracle