Assuming you have not backup after the delete, yes. However, Kindle has a function that will allow you to upload documents to your repository on the site via an email, assuming you have set up this functionality on the site.Once uploaded, it is "in the cloud" and can be downloaded to the iPad Kindle app. I'm not sure what the limitations are, but you might want to check into it.
Apparently it is NOT possibile to upload a .mobi file in the Kindle Reader app up to the Amazon cloud (could not find on Amazon support site, so spoke with Amazon support rep).
Amazon suggestion was to save the .mobi on the Mac/PC. I was able to get another copy of the .mobi from the bookstore, so this worked. It would not have worked if the .mobi document only existed on the iPad.
Solution was to purchase the book on the Mac/PC. Save the downloaded .mobi file; mail the .mobi file to myself, then select the Kindle Reader when prompted to download it to the iPad.
Not sure if this would work if there were was "protection" on the file to prevent further "free" distribution.
I still wonder though if the book/document might be stored with the data with the Kindle Reader app as part of the iPad backup.