IMAP push (IMAP IDLE as it's called in the IMAP spec) -- is part (extension) of the IMAP protocol.
POP3 is an entirely different, unrelated, mail protocol.
So -- correct, if you use POP3, you will be using POP3, and not IMAP.
POP3: no push, no folders, no back-sync of read/unread/starred/answered/forwarded flags.
IMAP: push, folders, back-sync of read/unread/starred/answered/forwarded flags.