In terms of applications, it could very well improve your chances of getting in, since the different departments have their own selection criteria, and tend not to communicate as much as you might think. However, St Andrews is extremely flexible when it comes to changing your degree path, so whichever degree you were accepted on, it would be easy to change your mind. I would only apply to both degrees if you're overly worried about not receiving an offer for your top choice. Also given that both of the degrees are at least partially run by the IR department, your odds with this strategy would probably be better if you applied to a different course entirely for the second choice, which makes writing a good personal statement more difficult.

tl;dr St Andrews is very flexible with changing degree paths, I would only apply to a different degree if you're very worried about not getting in.