How important is it to build relationships beyond the marketing department?

It's critical to build relationships throughout the entire company, not just with marketing personnel. Get to know the salespeople especially, since they can tell you what marketing efforts actually help move product - which is ultimately the goal of marketing. Marketing people change companies frequently (for example, Hoonigan's marketing director came from Red Bull), so if you only know one person, you lose your contact when they leave. By knowing multiple people including sales staff, you maintain relationships and understand what truly creates value for the sponsor.