For now, no. POP3 is such a simple protocol you usually can just use it directly. If would be super difficult or in some parts impossible to emulate all the current features on top of a POP3 backend.
If you downloaded the messages locally you could.
Yes. Though IMAP API does not have a storage for emails. It only uses minimal storage for state caching, everything else is retrieved directly from the IMAP server. IMAP API also leverages IMAP server's capabilities for parsing, doing itself as less as possible.