If an app doesn't itself check periodically for updates, then there's nothing natively installed on the eDGe to check for app updates (other than the enTourage Update app which only checks for updates to the enTourage firmware and provides a notification if you have Auto Update Notification enabled).

However, both the Slideme.org and AndAppStore.com market apps will check for updates for apps you have installed that also exist in their markets (doesn't matter if you installed it from there) and give you the corresponding notification.