For the sake of clarification, what exactly do you want any mobile capability to be able to do? And who would be logging into it? Staff / students? etc.
And what are you looking for in a moodle integration - automated course enrolments/withdrawals? All courses automatically have a moodle page?
I know of institutions in the UK who have achieved both of the above, by using a mix of the Database Enrolment plugin (included in core moodle) and some custom development. We've looked at doing automatic course enrolments / withdrawals, but it's a time thing and would require changes to our MIS (QL, for the record).