Yes the two classes can compliment each other, particularly since you are looking to see what the cross over is going into the classes. Branding is an area of marketing that is highly related to psychology since one of the primary goals of branding is to have consumers remember and have favorable impressions of the advertiser's brand. Psychology can help answer the question of how to engage and appeal to the human psych. For example, what super bowl ad will make consumers most want to go out and buy my product. Got milk?
Absolutely agree. My Business degree where I specialised in marketing had a specific psychology module integrated. This relates closely to buyer behaviour so it is very important to understand the audience you are targeting and their social/human needs "Maslow's hierarchy of needs".
You have been given some excellent insights. My only additional thought to consider (based on my experience) is that understanding your customers whether business to business or business to consumer is essential to successful marketing efforts. It really sounds simple however in the crazy competitive business world things get rushed and often the "customer-understanding" aspects get left behind. By having a psychological background/education you will have the natural advantage of keeping it in the forefront of everything you do. This will help set you apart and keep the rest of the organization grounded in a customer-centric way.
Best of luck.