Greylisting is a mechanism that relies on the methods spammers must use to avoid permanent (and widely available) spam blacklists in order to prevent the spam from being received in the first place. Due to the fact that they must mail large numbers of addresses at once before their server is blacklisted, spammers use misconfigured mail servers and greylisting takes advantage of the fact that those servers do not resopnd properly to certain error messages to prevent the mail from being sent in the first place.
For all legitimate, properly configured mail servers, greylisting merely results in a (generally short) delay between in receipt of the message the very first time someone sends an email to a server using greylisting. Assuming the senders server replies properly, once the first message is finally delivered, all further messages from that sender will be delivered normally, as long as the credentials that were sent with their first message don’t change.