MOBI files are sent back with the wrong MIME type, "aapplication/x-mobipocket-ebook" and anyone trying to download it on a Kindle receives an error that says, "Web Browser cannot download this type of file. Only files with the extension .AZW, .PRC, .MOBI or .TXT can be downloaded to your Kindle." You can still download the file on another device and send it to your Kindle, though.
Once deployed, a Kindle user should be able to download MOBI files on their device. However, it's possible they may still encounter an error saying, "Web Browser is unable to establish a secure connection with this web site," which is likely unrelated.