No, I don't think he could. From my understanding everyone is born with one nature element, (fire,wind, ect.) Now many people can learn other nature elements and utilize those jutsus.
However, some people are born with 2 elements and this is where you get your KKG users like Haku for example. He was born with wind and water and is able to combine them to make ice, unlike someone who was born with wind, but learned water. He wouldn't be able to use ice because he wasn't born with both elements. As a matter of fact last weeks anime explains this fairly well. Another example is Kakashi he has both earth and water elements, but can't use wood style because he learned the elements through his sharnigan rather than being born with it.
I think the rinnengan just makes it easier to learn the nature elements, but because they weren't born with it they can't use things like dust release and wood style.