I'm not sure about compatibility with Elements 9. But IF ACR isn't fully compatible with Lightroom 4 then you can have Lightroom render a TIF file that includes all of the Lightroom adjustments and then open that in Elements. It works seamlessly. Even if Lightroom and Elements 9 were fully compatible, once you make changes in Elements a TIF or PSD file has to be created anyway. So you can work with Lightroom 4 and be completely productive with it.
Actually, the only way you can pass an image to PSE from LR is by rendering a TIFF/PSD file. There is no native interface for passign a Raw image to PSE. Therefore ACR in PSE will never be used for an image passed by LR, and therefore there won't be a compatibility issue.