I was wondering if there was a Group Policy I could create that would show this:
Now, nothing about the "Activate Windows now" messages. I just want to put custom information in the bottom right of their screen (where it says things like "Windows 7" and "Evaluation copy. Build 7100", etc.).
There is no in built method of doing this. If all your clients are the same then you could push out a static background policy, but this would overwrite any image they have.
Alternatively, you may be able to get your desired result by using something similar to BGInfo, though:
http://technet.microsoft.com/en-us/sysinternals/bb897557.aspx
BGInfo is definitely the way to go, you might just have to watch the timings of when you run it to make sure the info its showing is correct. You also have to accept its licence, but i think you can pass a command line param to do this