I'm assuming that you're using GMailSender as defined in this post.
Internally GMailSender calls Transport.send(message) which will throw an exception if the send to the GMail server is unsuccessful, but this is being caught and suppressed, so your calling code has no way of knowing whether sending was successful. Firstly you'll need to change the GMailSender code to do something a bit more meaningful in the case of a send error.
What you must remember is that email is not delivered directly to the final recipient by your app or even the GMail server. Just because you managed to send correctly to the GMail server, does not mean that it will actually reach its intended recipient, as it could fail at any mail relay on its route. To properly detect and report on whether mail actually reaches its destination you'll need something a little more sophisticated than this.
RFC 1891 is an extension to the SMTP protocol which supports delivery status notifications, but you may need to re-architect your app to be able to use this. Essentially it works by setting flags in your outgoing message to instruct mail relays to inform you of the message status. In order for you to receive this notification, you must essentially have your own mail server which is capable of receiving emails. You will receive an email containing, for example, a delivery report once a mail relay has successfully delivered it to the recipient's mailbox.
So, to properly implement this, you'll need a mail account for your app which will receive delivery status notifications. You'll need to create an SMTPMessage object, and add a header including a "Return-Receipt-To" header, whose value is set to this mail account. You'll also need to setNotifyOptions() on your message, and then send it to the GMail server. Your app will need to check its account periodically for delivery notifications.
This is a purely email-centric approach. Without knowing your precise requirements, there are alternate mechanisms that you can use. For example, if your requirement is purely to verify that an email address exists, then you can send an email which contains a URI to a server that you control. The URI contains parameters which uniquely identify both the user, and the installation of your app. The user must click on the link, and your server component verifies the mail account. It can then use something like C2DM to inform your app that the mail account is real and valid.
Sorry if this answer is a little long, and does not offer you a simple solution, but if you want to be able to properly determine whether mail is reaching its recipient, then there is no simple answer, I'm afraid.