No, it does not work like that. You will get different results. For example if you have the whole image and there is a lot of contrast in it - e.g. a glowing sphere, dark background, and some flat surface like a wall, then the same noise limit will be completely different when rendering the whole image, and when rendering a part of it (e.g. a part where the glowing sphere is visible, a part where the flat surface is visible, etc.).
I can see an issue here, but currently can't think of any reliable solution other than disabling adaptivity.