IPhone – ny way to get an email notification when someone leaves a voice mail

There might be another app that will work, eNotify. While I haven't tried it there is a lite version you can use to see if it works for you. This is along the think different solution. Send the email to a special email account and get annoying alerts.

eNotify provides direct local notification for incoming messages along with custom email alert sounds for different accounts, senders, subjects, and recipient addresses. Easily silence background email noise and stay aware of important message traffic! In addition, the message sender and subject can be shown via local notice, so you'll always know when your spouse wants you to drop by the store on the way home, without unlocking your phone!

You could just use temporary screen pop-ups, and disable the notification center:

You can set this per app.

Apple Menu -> System Preferences -> Notifications

Then, for Sparrow, choose Banners, not alerts.