Can I take the CSM and CSPO courses back-to-back?

Yes, people often take the courses back to back. There is very little actual overlap between the two courses. There is, of course, some conceptual overlap in some concepts (for example, user stories) that need to be covered in both classes. But, those concepts are taught in different ways with different examples and exercises in the two courses. 

In many ways the two courses are complementary because the Certified ScrumMaster course is focused on the mechanics of Scrum and, as such, is really appropriate for any team member. The Certified Scrum Product Owner course is focused very specifically on the role of the product owner. It does not, therefore, cover the mechanics of Scrum at all as participants are assumed to know the mechanics through having worked with a team or perhaps by taking a ScrumMaster course.