The Official Google Blog has a post on the carbon footprint in a Google's data center to support a Gmail account.
The data Google uses is:
We compared Gmail to the traditional enterprise email solutions it’s replaced for more than 4 million businesses. The results were clear: switching to Gmail can be almost 80 times more energy efficient than running in-house email. This is because cloud-based services are typically housed in highly efficient data centers that operate at higher server utilization rates and use hardware and software that’s built specifically for the services they provide—conditions that small businesses are rarely able to create on their own.
An illustration of inefficient server utilization by smaller companies compared to efficient utilization in the cloud.
Your carbon footprint is most likely larger for the device you use than what is in the cloud.
In calculating these numbers, we included the energy used by all the Google infrastructure supporting Gmail and YouTube. Of course, your own laptop or phone also consumes energy while you’re accessing Google, so it’s important to choose an efficient model.
If you wanted you could reverse calculate the number of users per server you can use the 1.2kg CO2 is X amount of kw-hr. A Google server with PUE and Overhead and IT infrastructure could be 250 watts per server. Calculate the # of kw-hrs over a year. There are most likely 3 instances running your gmail account, so you may need to multiply by three. Then you can come up with an estimate of how many users can be supported by a gmail server.