I am developing mobile client for emailing service. One of the key features is notifications about new messages in the mailbox. As recommended by GCM architecture guidelines
Google does not make these statistics available to you. There are some statistics available on the android developer console. This only shows the number of messages and registrations.
You would have to implement your own data collection, which could be done fairly easily. You could record the time & id of each message sent and have your android client report back to your server with the time of message receipt. You could then store the data on your server and query as needed.