Would borrowing a torah book (without permission) from a shul be considered mitzvah haba b'averah if you use it to learn from ?
There are a number of different circumstances that would occur that would allow someone to use a sefer in shul without explicitly asking permission. The question however, seems to imply that someone has taken the sefer from the shul without first asking permission. Thus, using a sefer (that belongs to someone) in the shul is different than taking a sefer home from the shul without asking permission or notifying someone (such as the rav or the gabbai) who has the authority to allow it.
If this is done, you have prevented someone else from being able to use it. That is why someone who uses a sefer in shul should return it to the shelf where it belongs.