Kudzu is an invasive species because it out-competes other types of flora. It is not an invasive species purely because of human control. True, humans have helped it affect other species by moving them, but if Kudzu somehow (perhaps a form of geological change happens in thousands of years like a land bridge, or continental shift, or maybe the seeds are simply moved by some migrating population of bird) reached these new ecosystems by it's own means, it would still be an invasive species.
My point is that unless there is some way to restrict which 'biomes' different organisms can inhabit, some invasive species will outcompete others, particularly if some less competitive species are evolved for specific niche environments only found on Earth. This segregation is not likely to happen naturally as it has on earth, and thus the idealistic diversity and preservation that yohann305 was hoping for wouldn't occur without human intervention and control.