The OneDrive Office Options
The OneDrive saving behavior is controlled on the Office tab of OneDrive settings. From the OneDrive system tray icon, right click and select Settings, then choose the Office tab:
Microsoft changes this regularly, and the options you see will depend on which version of Office and OneDrive you have installed. I have the Office 2016 option on a PC which has Office 2010 installed.
Other side-effects
Following dual screenshot shows changes in File
menu content in Word 2013 with above mentioned functionality turned off (above) and on (below).
In addition -- yes, you're correct -- the Pause syncing
option is removed from OneDrive's context menu, if integration with Office is enabled:
More information can be found in these:
and probably many more articles across the Internet.
Office 2016 Has OneDrive Integration Built-In
Also, you should be aware that even with these unticked, in Office 2016 the first suggested Save location is OneDrive on the web:
If you select to save into "OneDrive - Personal" Office will upload the file itself, which will then be downloaded to your PC by OneDrive. If you just want to save to the OneDrive folder on your PC and let the OneDrive app handle uploading it, you have to click Browse and select the OneDrive folder.