I've already asked this question, some interesting answers - see here:
http://stackoverflow.com/questions/3309835/alternative-solutions-for-in-house-iphone-enterprise-app-distribution
EDIT: I realise there is more to your question than what is answered in mine.
Yes, the client will need to get an enterprise license (Apple recently removed the 500 employee limit). Once he has the license, he will need to add you as a developer under his license. This will allow you to develop and digitially sign the app on your machine.
As for testing, when you enroll in an iOS development program, you can then generate + download the appropriate certificiates to sign an app for hardware testing. You'll need to install what's called a "Provising Profile" onto the testing device, then when you're in xcode, change the deployment type from "iPhoneSimulator" to "Device" - this will then compile + deploy the app in it's current state to the device. You can also install this Provising Profile onto other devices then send them the compiled app (which is installed via iTunes).
There is more to be found out about this by going to the Apple Developer Portal but I thought I'd give a brief overview of what you were asking.