It seems like you can assign this action to Ctrl + S, yes. See here:
Edit → Keyboard Shortcuts → file → Overwrite […]
I think this would be awful default behaviour, but I guess it’s nice to have the option if you really want it, and I was pleasantly surprised at how easy it was to find after reading your comment.
It used to be even simpler, though I am sure it caused all sorts of problems: for any Gtk+ program, if you hovered over a menu and pressed a new key combination, it would reassign the shortcut for that menu to what you just pressed. You still had to turn it on, and it was an amazing feature, but you'd occasionally reassign something you did not want to :)