I have a naturally quiet voice although I try to speak louder. would voice coaching help me speak louder?

Yes, it probably would.

When I was very young, I was a stage actor and learning how to speak with the diaphragm to project your voice in the theater without sounding like I was shouting the words really helped with that.

Some people grow up speaking loudly and it's natural for them. I've met people who always speak like they were talking in a crowded bar or a noisy room no matter where they were. How annoying is that?

They didn't speak quietly unless they were trying to coax somebody into doing them a favor.

It could also stem from you just being a bit shy. so taking voice lessons through oral interpretation classes or drama classes would help you a lot.