Slingbox requires component connection. The use of HDMI from cable box disables component output. So seems as all would be lost for getting Slingbox to work with Google TV. The best solution I've found is to get an HDFury3 that will convert the HDMI leaving the Google TV device and convert the signal to component. The only problem is that the HDFury3 is almost impossible to get in the US so you could order it and import it from another country. This HDMI to component adapter isn't cheap but it does work very nice.
Another solution is to wait for cable company to implement remote dvr access from another cable box in the home. So then you hook up the Slingbox to a different cable box than the Google TV so that you don't have the HDMI/component simultaneous use problem. This feature is coming soon from cable companies.
Thank you for your post. While the physical connection of the items is possible, there is no method for installing software on to the Sony Internet TV unit that will function as the go between to control the slingbox. And as the marketplace is not yet available, there is no Android app that can be used as well.