I am working for an organization and we would like to obtain an Enterprise Developer Account. I was wondering wether the enterprise developer iTunes Connect lets you view download statistics just like the normal company or individual version of iTunes Connect does.
No it doesn't. An enterprise program membership has no access to App Store Connect.
Enterprise apps are not distributed through the App Store.
You distribute them through a web server, MDM or direct installation to the device.
Apple has no visibility on app installations using these methods.
You will need to monitor app installations and use through other techniques such as analysing your server logs, using analytics in your app or reporting from your MDM.