mdl_enrol_authorize keeps track of enrolments.
In version 1.6, you will able to manage payments. Payment review is a big feature. After you accept the payment then student is enrolled to course. If you want to decline payment VOID it. If course cost is $100 and you mistakenly set up $1000 and a student paid for course. No problem. REFUND $900.
As you see, you can accept/deny/refund payments and all actions are stored. 1.6 will be released on beginning of March.
New features are here: