I'm planning on getting my undergraduate degree in Psychology. Could I still become a marketing manager?

It's possible. The job varies from place to place, but basically you manage the placement of items for high turn over.

In retail these are typically known as District Managers and they are generally hated by store managers who know their own areas and put things in places to make $$$ while the District MAnager want the poor selling items that don't make money up front so they can shovel them out and then ruins store profits in favor of item placement.