Putting an affiliate professor in statement of purpose
It may be difficult to have an affiliate professor as your sole adviser if he or she is not a professor housed in your main department. Administratively, it can be a challenge to have graduate students matriculated in one department but being advised by another. 

However, if the professor is an affiliate of the department, he/she likely has someone who is full-time in your target department that they work with. You could say something such as


  I am interested in working with Professors Carl McCauley [in main department] and Demelza Fordham [affiliate]. Their research on the decomposition of rubber aligns closely with the work I did on rubber composites while at the University of ZYX. 


If you tie them into a professor in your target department, being associated with an affiliated professor can actually be a good thing. It will give you more diversity and networking opportunities.  It may also fulfill requirements for outside committee members on your dissertation committee.