As far as I know, there should be no reason you couldn't do this. Once you pass the RMP exam, you can then apply some of the formal training hours for your PMP exam as PDUs for the RMP recertification.
"If you have an apple and I have an apple and we exchange apples then you and I will still each have one apple. But if you have an idea and I have an idea and we exchange these ideas, then each of us will have two ideas."