If you are only utilizing "Enable Auto Cron:" then it will only check for emails (and deal with client updating tickets, opening new tickets etc) when there is staff activity. Let's call this incoming for sake of clarity. Otherwise it is only checked based on how often you have cron running it (or Windows Task Scheduler depending on your ServerOS). We have task scheduler running every minute, which is probably a little excessive. If you have not setup a cron/tasksched and are not using auto cron, then it will never check for emails.
All of this has nothing to do with outgoing emails from staff updating tickets.
Those emails are sent immediately. If it is not, then it is not a problem with osticket. It could be any number of things (including but not limited to: mail server congestion, spam filtering, viri scanning, etc).
