The correlation between the event mean-transverse momentum, [pT], and the anisotropic flow magnitude, vn, ρ(v 2 n , [pT ]), has been argued to be sensitive to the initial conditions in heavy-ion collisions. We use simulated events generated with the AMPT and EPOS models, to investigate the model dependence, and the response and sensitivity of the ρ(v 2 2 , [pT ]) correlator to collisionsystem size and shape, and the viscosity of the matter produced in the collisions. We find good qualitative agreement between the correlators for the string melting version of the AMPT model and the EPOS model. Detailed tests indicate that ρ(v 2 2 , [pT ]) is sensitive to the initial-state geometry of the collision system, but is insensitive to sizable changes in the viscosity of the medium produced in the collisions. These findings suggest that precise differential measurements of ρ(v 2 2 , [pT ]) as a function of system-size, shape and beam-energy could provide more stringent constraints to discern between initial-state models and hence, more reliable extractions of η/s.