When you define a template and a component - the template references the component. That is - the ResourceType -- which is the component's path that is assigned to the template. Moving the component will break the reference between a template and a component.
Its not really good to move a components path. But if you have to sometime - you need to update the ResourceType of the component. To do that - you can do it manually in CRXDE lite. Or you can modify the properties using the JCR API.