If you were willing to forego just the one modifier key and instead use CMD-§ (or any other combination), then the following would be a work-around. As always, there are probably more elegant solutions!
1st Macro Hotkey (F20) with just the Search the web with keyword action.
2nd Macro Hotkey (CMD-F20) Load google homepage
If you hit F20 and then decide you want the homepage, CMD-F20 will cancel that macro and load google homepage.
The attached macro has some unnecessary cancel action steps and different hotkeys. Hope that helps. I think the issue is that once you have executed the macro, it is done, it's not sitting there waiting for another keystroke. That would take something more complicated. My solution, while not elegant, does what you ask I think at the expense of an extra keystroke.
Thanks, not only Google, but also a lot of websites need to be set up like Quora.com and keyboardmaestro.com, sometimes keyword search, sometimes open the home page to see new posts. thank you very much!