In this paper, we investigate how additive noise, e.g. thermomechanical noise, impacts the resolution of mode-localized resonant sensing architectures based on two weakly-coupled resonators. Existing work suggests that the resolution of these sensors can be improved by decreasing the coupling coefficient of the resonators. The present work gives an analytical proof that this result does not hold when the ratio of the motional amplitudes of the resonators is used as an output metric, and that, in this case, the sensor resolution is actually independent of the coupling strength. We then extend our proof, supported by transient simulations of a simple model, to other output metrics.