Hi @guava01
Yes, messages are still delivered to you while you are offline. Depending on your notification settings, you can receive email and push notifications for messages that are delivered while you are away from Mattermost. You can read about setting up notifications here: http://docs.mattermost.com/help/settings/account-settings.html#notifications
If you'd like to keep Mattermost with you while you're away from your desk, you can download our mobile apps here: https://www.mattermost.org/community-applications/#native