Depends on the type of music and even the song. I can remember needing to count during certain parts of certain songs.
I did have the opportunity to drum for Evita (the show,) once. Would love to do it again. I DID have to think for that show. There are a lot of things, and odd time signatures, going on, and some of the stuff I just had to count.
If you can read and you have the opportunity to do some musicals, even for a local group, it is quite a nice change of pace. I used to do a lot of them, and loved them.