Importing a site to your stage environment would be possible and it would basically overwrite your current instance. However, the primary keys (IDs) could and will be different than the ones you had before. I'm not sure how your site is developed, but it is recommended to avoid storing ID's in database to create relations as this could be problematic (use GUIDs instead).
If this will be an issue I think you will need to manually update the documents/page templates. I would avoid using SQL updates directly and used API instead to update objects.