As I understand an Intel vPro based computer can be powered on remotely without the use of a 'magic packet', the management controller is sitting in a low powered state listening on specific ports. Therefore I'm assuming that the management controller is sharing the IP address of the host that is shut down.
Does the management controller maintain this IP address continually renewing it after the lease expires?
I believe you are specifically speaking about AMT, which is, in Wikipedia's words, "the most visible component of vPro".
I haven't used it directly, but from my research about it, it is "out of band" management, much like a Dell DRAC card, or an IPMI card that have been used for years. Specifically, the "Hardware-based Features in AMT" section in Wikipedia's article on AMT says that the boot is OOB. So it's more like a management co-processor, rather than something like Wake On LAN.
By "out of band" (OOB), it means that the co-processor would have it's own IP engine that was always running and had an IP different than the PC. Again, this is my understanding from reading about it, I haven't had any hardware that implements it yet.
Essentially AMT, the vPro feature that allows for remote power on, has its own processor. This is often called the Manageability Engine (ME). It can request DHCP addresses. At the same time, it's smart enough to know when the OS has control of the NIC. In that case, it lets the OS handle DHCP and just uses the same IP. When the OS is down (system is off, or NIC driver is not installed or failing), AMT will take over making DHCP requests as needed.