The extension or background will simply not render.
There are options to have tile servers (the "drawings" of the maps) locally, so you don't need access to the Internet. I don't know if that's possible with Google's and how big the cluster of servers would need to be to host that information.
If you are using the scatter object with dynamic background, it requires internet access for the background, however the bubbles will display on a blank chart in the right location with the right size, if an expression has been defined for their size.
If you are using an extension, you need full access to Internet as it is something.google.com which replies and displays the points or routes on screen.
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