@Rainbow Carnage - I'm not sure specifically about the Playbill, but I was told that it's fine to send fanmail to the theater. My husband was nice enough to run in to the Belasco and ask while we were on our way to the airport to fly home, and he said the guy said people do it all the time and he does receive it.
I feel you - it's something I very rarely consider doing too, but JCM was so incredible and he was so sweet at the stage door (I gave him something after the 10pm show last Friday, and he graciously took a picture with me, which I didn't find out until afterwards is apparently a very rare occurrence), and I'd really like to write him to say thank you and let him know how much it and his performance meant to me.