No. The default value only applies when you first add the Component to your Layout canvas. It will not propagate to existing instances of your Component.
You can set a default value for Component fields. The default value is applied when you add the Component to your Layout canvas. For example, if you have a Component with a Color picker field and you select a default value of Red, this will apply Red when you use the Component.
If you change the default value to Blue, all new instances of the Component will use Blue but all existing instances of the Component will use Red.
This behavior is by design. This is because it would be dangerous to assume that a change to the Default value in the Component should run through all pages and all existing instances of a Component and alter their appearance.