I think, have the guy go to the training, if you do not then you will be the one he comes to when he doesn't have the training with questions. Also, your vendor will make a big difference. If you do not go for the Avaya training, budget for additional admin training from your vendor.
Talk to the project manager from your vendor about it. I have done this in the office before and it works great. I pre-program the new system, then I have the customers admin person in to the office a couple days before the install.
I with intent leave some items not programmed, like date, time, etc., I then have the customer admin do a back up, and then program these items, then restore and program them again. They take notes in their own documentation that comes with the system. I walk them through the process, and train them rather than teach them. When the phone system goes in they have already done all the basic admin functions and it makes them feel very confident, which is half the battle with many people. I do the same with the voice mail.
During the install, I have the sytem admin do most of the user training with me, because training someone is the best way to learn something.
Works for me and have never had a customer complain about being billed for my time to do this. I still offer admin training time which would nornaly come with a system install, but it generaly goes more in depth, and gets into MAC's more. Often times the changes that are requested after the install, which sometimes come, I use to further train them.