Firstly, bad breath can be due to many reasons. And actually the most common cause of bad breath will be dehydration. Not drinking enough water.
Secondly, it could be due to food getting stuck in teeth and not getting cleaned out properly when you are brushing.
So, does braces help with bad breath? Actually they can make it worse. Because more food can get stuck in them.
The exception is that your teeth are so crowded that you have trouble cleaning them properly, then you get braces and you can clean your teeth properly, then yes that helps.
By and large, it's not a solution for bad breath without finding out the cause of bad breath first.