Uninstalling Chrome will not delete desktop shortcuts to websites unless you manually remove them. It is possible that some Web Apps may be delete with Chrome(Like Spotify Web, Twitter).
For the Error (0X80004005) :
Try running chrome with Admin Rights and then go to chrome://settings/help and try updating again.
Alternative is Using Google's Chrome Cleanup Tool.
Reinstall latest Chrome:
Download from: https://www.google.com/chrome/