OP here with some additional information regarding this ongoing problem.
I realized that by default, the Alerts service was configured to send out e-mails notifying of various problems (disk unreachable, disk space, virus detected, etc). I unchecked all the boxes for E-mail notification, and for good measure, erased the Recipient e-mail address that appears on the Alerts screen. Alas, this made no difference. The same "IMAP factory connection failed" error is still getting generated every 30 seconds.
Perhaps an undocumented required for ML Server is that the Mail service has to be activated?? If so, why would Apple provide an ON/OFF switch for the Mail service? There must be some way to disable ML Server from attempting to make an IMAP connection.