Sideloaded books, whether AZW3 or MOBI, will always display covers, and calibre can set them to not show the Personal banner by setting the cdetype to EBOK. But of course they won't sync.
If you send them to your Kindle email, in order to get whispersync, you can send only .mobis, but that can be old MOBI or dual-MOBI.
A dual-MOBI will be split, and send AZW3 to supported devices, and MOBI to the older devices that don't support AZW3.
A MOBI will always be MOBI.
The MOBI will show a cover, the AZW3 will not. Either way, there will be a Personal banner, since no matter what you email them, Amazon will post-process the files to set the cdetype to PDOC.
Hope this helps clear things up.
P.S. quiris has created a helper program to set missing covers for Whispersynced personal documents. See this thread for more details, especially post #14:
https://www.mobileread.com/forums/sho...d.php?t=212242