I've worked around the issue for now, but I'd like to report what I'm pretty sure is a bug. Here are my steps to reproduce:
1) Start vmware vSphere Client 5.5
2) Clone a machine with Windows Server 2012 with DHCP. (I don't know if DHCP is required for the bug.) "Image A". Set it up to have network access.
3) Remove From Inventory, Download vmx file, add the below lines, and Add to Inventory.
vhv.enable = "TRUE"
hypervisor.cpuid.v0 = "FALSE"
4) Power on the image and launch Virtual Machine Console
5) Start the Server Manager if it doesn't launch automatically on login.
6) "Add Roles and Features". On the "Server Roles" page, add "Hyper-V". You'll be guided to setup a Virtual Switch. Do it. Don't change any other defaults.
7) After this is completely installed (requires a restart), shut down guest.
8) Clone machine in vSphere. "Image B"
9) Power On both images and login.
Image A will have network access. Image B will NOT have network access.