Oh dear! I'm not sure I should respond because I held up the counter installation process while waiting for the Lee Valley unit to arrive (during the Christmas shipping rush, much to my annoyance!). But thinking back on it, I believe that it is possible to install post-counter. This will depend on how wide your door opening is, and how wide the installer is. Do you have a smart dog that can use a drill?

You need to be able to access the back wall of the cabinet, including the corner farthest from the door. It's probably an easier reach from an open topped cabinet, but I bet some people would be able to squeeze into the space and screw the thing in.
Kathy