Yes if your smartphone is off it could still be a problem. AFAIK Sync in chrome is done by each device constantly listening in case another device does something (unlike Firefox sync which I think, but might be corrected by @Winapp2.ini, happens at program open/close)
I checked my system tray but cannot see any related icons to Google.
However even when I close Google Chrome there are still 20 instances of Chrome in my Task Manager and I just cannot 'end task' on them as they keep creating the process again.
I disabled the sync on my mobile phone to see if that will help but it didn't.
I haven't ran my PC in Safe Mode for a while now but when I next do I will try the cleaner again and update you accordingly.