I just discovered a way to sideload MOBI files to Kindle for iPad on a non-jailbroken iDevice.
Macroplant offers a free app 'iPhone Explorer'
which allows you to browse the contents of your connected iDevice.
When you open your iDevice with iPhone Explorer, there are two folders - Apps and Media.
Inside the Apps folder is a Kindle folder (assuming you've installed Kindle for iPad), and within you will find Documents/eBooks. For those of you playing at home, the full path is Apps/Kindle/Documents/eBooks.
I dropped a MOBI into that folder, and lo and behold, that MOBI can be opened in the Kindle for iPad app.
iPhone Explorer occasionally crashes when dropping the file into the folder, and it appears that all sideloaded files share the same cover, but hey, you gotta start somewhere.