That would be unlikely. In order for the user to read the emails, they would have to be delivered to some final destination, e.g. a mailbox file or maildir or other type of local email storage, from which they are accessible via POP, IMAP and/or some webmail contraption.
The emails at your secondary MX are simply being queued up; they are never delivered to anybody's mailbox or maildir.
As for bouncebacks, generally speaking having a secondary MX will make little or no difference. If your server is down (as in "doesn't respond at all"), and there is no secondary MX, the sending mailserver should keep trying to send the message for some time. Exactly how long is up to the sysadmin of that server; it's common to have up to a week. The only time that a secondary mailserver would be useful is if your primary mailserver is likely to be down for more than a couple of days, and the secondary MX will keep the queue for you for longer than that.