Is a valid USB VID/PID necessary for strictly embedded use of the Bus?

It will work, if that's what you're asking. And there is no law saying you must buy a VID from the USB-IF in order to use USB - you only get in trouble if you use the name and logo without permission. Some things to consider:

• If you do want to insert a computer, to do debugging or something, life will be easier if you have a unique VID/PID combo and can write drivers accordingly.
• At some point one of your customers will take the product apart and, if they see a USB port inside, plug it into a computer. They shouldn't have any drivers for that VID, but they might. You'll want to make sure that can't damage anything, or just stick a "warranty void if opened" sticker on it.
• The same is true if the user can plug random hardware into the USB host within the device. They shouldn't have any hardware with that VID, but they might. And you don't want the host to brick that hardware by accident. If there are no external USB ports, then the warranty void sticker works here too.
• Some dodgy USB sticks and other cheap clone devices use VID=6666 and PID=8888, and maybe others. It's probably worth checking and avoiding those PIDs.
• You can buy single PIDs from MCS electronics for about $15. The USB-IF do not approve, but legally it seems they cannot stop it. Some manufacturers of USB hardware also give out PIDs from their VID.

That said, I'd probably just do what you propose, and use VID=6666 with some random (i.e. not 1111 or BEEF etc) PID which doesn't have any google hits.

No, you don't need a unique VID/PID. These parameters are used by the OS to load the correct driver for the device. If you don't need a driver, you don't need these parameters.

If any of the following are true:

• your internal use of the USB bus needs to be certified compliant with the USB specification
• you need to use the logo and/or other trademarks associated with the USB standard
• you want your device/host to work with 3rd party USB devices

Then yes, you will need to comply with the VID/PID requirements as well.

If all three are false then you can use whatever VID/PID you want that will meet your project requirements.