Can Jackrabbit automatically post the class tuition(s)?

Yes, it can!  Under Tools > Edit Settings > Tuition Settings > Tuition Fee Settings, you have the option to post full tuition, post discounted tuition (if you discount), post prorated tuition (if you prorate), or post discounted and prorated tuition.   Based on your settings, tuition will post when a student enrolls during web registration, quick registration, or via the Parent Portal.