Hi,
The reason we require the IP addresses is that we have all internet access completely shut down, so there is no way for our site to send out a call to Google Analytics each time a user loads the page unless the IP address of the google servers have been added to our whitelist, therefore allowing data out from our network to theirs.
I did a bunch of research after initially asking the question back in November and it apparently there are no specific IP ranges for just Google Analytics related servers (they are just part of the overall server farm). We would need to whitelist well over a 100,000 ip addresses based on the ranges I found.
Thank you,
Heather