Lazors (2008) just says that you need passes in all theoretical knowledge subjects before undertaking the Skill Test. Not sure if this has since been updated.
Forget LASORS - even when it's up to date it's packed with errors. The real requirement is in JAR-FCL 1.030(e), which reads:
Before a skill test for the issue of a licence or rating is taken the applicant shall have passed the associated theoretical knowledge examination, provided that exceptions may be made by the Authority for applicants undergoing a course of integrated flying training.
So the answer to the original question is that it
is possible to start CPL flight training without all ATPL Theoretical Knowledge passes. However, I fully agree with Whirls and clearprop - it would not be a very clever idea to do so.