Not exactly:
As we mentioned before, the API grade refers to minimal yield stress required (SMYS), and there are an specific interval where yield strength and Ultimate tensile strength can belong to each grade, but, there are other properties like toughness (represented by CVN Energy or DWT), ductility (represented by elongation in tension test and shear fracture in impact test), where API only specifies minimal values for each grade and each one could be improved by different delivery condition and the user must be establish optimal levels based on the requirements of the engineering design for the specific pipeline.
Other properties like hardness will be different in each delivery condition, maybe higher in Quenched and tempered steel, and this property are important where you could have friction, erosion, impacts but shall be well controlled if there is probability of SSC or hydrogen damage by example.
The use of Q grades involves also the need for more controlled welding procedures, to avoid undesirable effects in each weld.
Finally, some studies try to establish relationships between microstructure (the microstructure is probably the main difference between each delivery condition) and corrosion resistance and how could be improved.
Summary: You must order M, N or Q grades when the engineering design for the specific pipeline demands it.