I have a number of customers who have agents with two lines as you mentioned.
1. Contact center line, no call waiting, no voice mail, auto answer
2. Private line, Unity, call waiting
Non-agents have just one line, configured as in 2.
The contact center line is not reachable from the private lines. Internal route points exist so that back-office staff can transfer a customer into the queuing platform so it ends up with agents on line 1. Contact center calls are normally not transferred to private lines.
It's difficult to marry the demands of contact centers with the need to send a given call to a particular agent. If you transfer to the private line, the call just disappears out of ICM.
There is nothing wrong with one contact centre agent transferring to another contact centre agent. The information is in the TCD and WebView. It will be far worse if you transfer to the private line.
For the customers who have these two lines, UCCE 8.0 introduces the ability for ICM to manage the two lines a bit better. We don't worry about it - agents have very strict instructions.
(a) if a call arrives on their private line while on a call, the ignore it and it goes to voice mail
(b) if a call arrives on their private line while in the ready state, they first go not ready and then answer the call
(c) if they want to make an outbound call on their private line, they go not ready
Some of the better agents break (b) but are prepared to drop the private line when a CC call arrives.
If your agents don't have Unity voice mail, two lines doesn't add anything really, and I would skip it.