No because both consoles use there own low level api, mantle is designed to bring a low level api to the pc to bypass directx's high overheads improve performance and to get the best out of the graphics architecture its employed on
It's ambitious for AMD to do, but it's going to fail hard. It's open to nVidia, but they are not going to adapt to the requirements of Mantle and change their hardware when they have the powerful Maxwell all ready around the corner and when that is succesful, then Mantle doesn't have a single chance on its own when AMD doesn't have any chance to get a larger market share. OpenGL with all its cumbersome extensions will then still be prefered due to this nature. But MS is looking closely at Mantle and will surely implement more features to make lower level access possible on each specific brand of cards when possible as they are already in the process of doing so for the Xbox One.