Can you transfer a Windows 7 XP-mode VHD to a new PC without the need for reactivation?

Absolutely.

If you can emulate the exact same environment you had before, you will not be prompted to reactive. Windows only asks you to reactivate if there were serious hardware changes, which could include any combination of switching your motherboard, processor, RAM, hard drives, etc. Because you have a VHD, all of this information will remain the same unless you decide to modify your virtual environment (i.e. add more processor cores, change the RAM, etc.)

Once you are up and running and have tested without any activation issues, save a backup and then try to increase your RAM. (I am assuming that you will have more memory in the new computer and would want to do this.) If that is all you change, you shouldn't have any issues.

(Other thoughts - I have been unable to locate any language on Microsoft's website to concur with this, but I can say that I have moved VHDs dozens of times between computers without a problem.)