I there a way to search exchange databases for large attachments and export the list to csv using powershell?

Tha

There is a way.  The way I did it was to write a script that walks through all mailboxes, opens them and iterates all messages using Exchange Web Services.  The script runs under PowerShell but the Exchange cmdlets aren't sufficient, hence the need to write EWS code.  I'm sorry, but I'm not able to share the script, but with some time and practice you should be able to code your own.

Hi.  As a colleague said above. For information on the investment required is large enough script. An example of the script.

Exchange Attachment statistics reporting with EWS and Powershell

Yep as Ed and Oleg mention EWS is the way to accomplish this with MS, however if your interested in 3rd party utilities to make this happen our DigiScope product http://www.lucid8.com/product/digiscope.asp provides an easy and intuitive way to accomplish the desired goal and more

Thank you for your example. Unfortunately I can not know all third-party software for Exchange 2013.

For large messages are used (archive mailbox rules), has an archive mailbox, if it is available.