Distribute App in House

Enterprise Program has no limit of devices you can test (deploy) your apps on. Normal Developers Program has a limit of 100 devices.

Say you will only have less then 100 devices in your company you can go with the normal Program otherwise you will need the Enterprise Program.

I highly recommend https://testflightapp.com/ for what you plan.

You can invite the employees by sending an email to them. They register at https://testflightapp.com/ and can download the app onto their devices. They get notifications for updates through email, too. You just need to upload your ipas to https://testflightapp.com/ for that.

If we deploy an app in house does it still need submitting to Apple or does this method overcome this problem?

No it does not require submitting to Apple.

Are there any additional requirements?

Yes, you need an Enterprise developer account. Require your own server to host the apps and need to implement method of distribution. You can also opt for 3rd party MDM services who manage the entire server part for you. But there is a cost involved.

What limitations are there if any over publishing to the app store?

In house signed apps install on any devices without having to add the UDID. Downside to this is illegal distribution of your app, hence the need for secured server or authenticated downloading. Also the enterprise account expires after one year, the apps need to be distributed again with the renewed in-house provisioning.

You can go through Distributing Enterprise Apps for iOS Devices for In-house distribution.

Hope that helps!