Reverse engineering tools like Scan to 3D (available in Premium or Pro versions) can help with meshes. However, in the case the leaves I think are problematic because they are most likely individual single surface objects. It is likely the branches are all separate objects as well, but have not looked at it yet.
I think this would require a lot of prep work in a mesh modeling application, like Blender, to be able to use any reverse engineering tool that can generate nurbs surfaces from meshes.
I think you will need to budget many hours to convert this to a useable model, and that's assuming you already have a tool to convert meshes to nurbs. Or, hire someone that can do it for you.
OK, I looked at your file. Its possible an application that is designed to make 3d printable objects might help, Like Netfabb or CadSpan. But the result of that would be a mesh.
How many triangles are in the file?
I can't get that info from the imported mesh in SolidWorks.
It possible that if the triangle count was low enough, like 15,000 or so, it might work assuming the mesh was a solid. Its possible to break up larger meshes into solid pieces containing about 15,000 triangles BEFORE they are imported into SolidWorks.