Yes, there is an ADIF download of your InBox. But I caution you to be EXTREMELY careful with it. You have to understand what it is. It is not YOUR logbook, but a consolidation of the logbooks of the people who have sent you cards. Thus, some of the entries in ADIF format are REVERSED. For example, CALL will be the callsign of the sender of the card. If we put CALL in the correct direction, every one of the records would have YOUR callsign under the CALL tag, and there would be no way to identify the sender.
So, go here
http://www.eqsl.cc/qslcard/downloadInBox.cfm but make sure to read the warnings at the bottom of the page, and make sure you understand the impact of whatever you're planning to do with the file.
Of course, that's just my opinion... I could be wrong!
73,
Dave Morris, N5UP