I've noticed that most MD/PhD's will consider you for MD admissions should you be rejected from MD/PhD. Do any programs consider you for PhD in that case? Or would you have to submit two separate applications for this particular "backup?"
It depends on the program. At no school is the consideration for PhD automatic after a MD/PhD waitlist or rejection. At many schools, a separate application is required for PhD programs that includes a GRE requirement. At some schools, you can be considered for PhD by request with a MD/PhD application.
I'm afraid you will have to check the policy at each school to which you apply. I believe that you will find most will have separate PhD-only applications.