iTunes Connect, check total sales?

From the Apple User Guide for the Financial Reports (available at bottom of iTunes Connect page):

We do not store or regenerate the data after the periods have expired (14 rolling days and 13 rolling weeks); you will need to download and store this data on a regular basis if you intend to use it in the future.

So the answer is: no. It's so ridiculous -- 500GB of storage costs peanuts (yes I know IT storage costs more, redundancy, management, backups, archiving, blah blah, etc.), but it's still cheap. Apple could keep a "total shipped" record and it wouldn't hurt them.

You might want to have a look in the section "Payments and Financial Reports" within iTunes Connect. There's an overview of your total sales within the "Summary" tab . However this view is only updated on a monthly basis.

From the "Sales and Trends" iTunes Connect FAQ

How long are reports available for download? Weekly Report: Thirteen (13) rolling weeks prior to the current week are available for download.

Daily Report: Seven (7) rolling days prior to the current day are available for download.

Information is only available for the periods following the date when the reporting was activated in iTunes Connect. Reporting is generally activated prior to any sales on the App Store.