The constraint is that you need to have passed ATPL theory to start a JAA type rating for a multi-pilot type. Although the ATPL theory pass doesn't show on your licence it does show up on the CAA's computers - if you tried to do a course without having passed the exams at ATPL level they wouldn't issue the type rating.
Because the regulations relating to the type rating do not require ATPL theory to be current in any way - you just have to have passed ATPL theory at some stage in the past - you can get a job with an airline holding only a CPL IR with expired ATPL exams and then, when you have the hours and before you get command, you can retake the ATPL exams.