The reality is that users aren't necessarily aware that their keystrokes (and any unintentionally pasted input) are being sent to Google long before they explic

The reality is that users aren't necessarily aware that their keystrokes (and any unintentionally pasted input) are being sent to Google long before they explicitly navigate anywhere. Inspect the network activity and you will see a log of individual keystrokes (depending on how quickly you type) sent to Google. Firefox waits until you have 2 characters in the address bar before they send them off.