Yes it does, but it is important to understand that even so the vast majority of the parts of the brain used are used for both and there is no evidence of a common physical cause of stammering. That is, while there are many types of brain damage - strokes etc - that can lead to stammering the vast majority of people who stammer have undamaged brains, so far as anyone has been able to tell. The causes seem to be psychological and habitual rather than physical.

The foreign language one is confusing; in my experience there is no very strong pattern: I know quite a few people who stammer in both and other who only stammer in their native language. While hesitating is of course common, I have never heard of anyone who only stammers in a foreign language.