If a Chrome Extension is installed but turned off, can it still spy on me?

Solution 1:

When an extension is turned off, it is not loaded into memory, and as such can't do anything.

When you turn an extension on, it has access to your entire browser history, and if an extension wants, it can submit your entire history to the server.

It depends on the extension if it really will do this. Spyware type extensions will, extensions that are meant to help you will usually only submit a website you are currently browsing, but whether or not an extension will do or not is purely speculation.

If you want to be safe and not want to allow an extension to transmit your data to their server, don't turn it on, ever.