Distribution of the enterprise iOS application
An app is just a file. You can distribute them through a sophisticated framework such as a custom App store hosted on your own servers or just place them on a web server. In fact, you could also just email the app or push them through iTunes or other file sharing technology.

When you sign up as any iOS developer - you can install apps on your devices without ever submitting them to Apple. In the case of an enterprise account, you are allowed to install them for production use as well as development use.

The mechanism you choose for Mobile Device Management will affect your costs and benefits for the various distribution methods, but your general question is answered - Yes, as an enterprise developer no Apple involvement is needed or possible if you don't want your apps ever on the App Store in general or getting reviewed by Apple in specific.