Personally I wouldn't apply until I've got the blue book - there's always a possibilty that you are in the right place at the right time, when you haven't even passed the CPL or IR....
MCC - I'd do independently. It's another string to your bow and 99 % of newly qualified CPL's go and get one.
Finally - it's a Frozen ATPL. Last year some twentysomething called our airline and got through to me - adamant he had an ATPL (despite only having 200 hrs) - I corrected him and duly told him to sod off..........
If you don't even know what licence you have, there's no hope!