No. The standard measurements are insufficient to capture all the subtleties of how we hear, and the variation among humans, and listening conditions. As was noted before by others, standard measurements are mainly error checks on design or implementation. Once measurements are close enough to ideal, the variation between systems that is left is still there, but no longer measurable. However, human hearing under the right conditions and listener training can detect differences that are beyond the "skill" of standard measurements.
When I was a kid in college, I helped civil engineers with coding. Back then, computers, numerical methods, or test rigs were not capable enough to measure and model anything but linear dynamics. But the engineers I worked with still did not ignore nonlinear plastic deformation in their designs, often by trial and error with scale models and drawing from the practical wisdom of their elders. Two designs that "measured the same" could definitely behave differently under conditions beyond the quantitative tools available then. Quite a few of the infamous disasters in civil engineering came from people believing their limited math and measurements too much,
My work over the last several decades has been on systems for search, speech recognition, pattern recognition where the work is all driven by measurement, A/B tests, ... Still we understand very well that A and B may measure similarly in all the standard metrics, and still behave very differently in practice.