I've never heard of anyone doing this and I don't think there is an easy way to find this information. Once thing you might consider doing is sending to an email address (maybe a gmail account) on all of your alerts to see how many have been sent over a specific time period. Obviously this won't give you any histortical data, but you can start tracking email volumes without needing to save them in your primary mailbox.
There are SMTP Performance counters available.
Refer to How to Check the SMTP Performance Counters in order to see how to view what counters are available. On our Solarwinds test box it looks like there are "Messages Delivered Total" and "Messages Sent Total" performance counters available.
I'm not really sure what the difference is between the two. I believe that these counts will reset to 0 whenever the service is restarted, so it might be a good idea to collect the data somewhere that won't be affected by server restarts.