No, it meets ENGINE test requirements. The LSPI test is in an actual running engine.
API SQ has certain concentration limits within the formulations. 800ppm max Phosphorus, 0.9% SAPS maximum, Sulphur, 0.5% for 0w and 5w grades.
The rest of the API SQ requirements are performance based. Which means that if you can pass all the performance tests but do not meet the chemical constraints, you have the situation of the ESP formulation-- it meets "engine test requirements" for API SQ, but because it busts some of the chemistry limits of the spec, it cannot be said to be fully API SQ compliant and cannot carry the "donut" for API SQ.