While numerous scattering and theological studies have investigated the disordering mechanism of low-molecular-weight poly(styrene-b-isoprene) (SI) diblock copolymers, relatively few efforts have addressed the real-space morphologies and transport properties of such copolymers at conditions near the order-disorder transition (ODT). In this work, the morphological features of seven compositionally symmetric (50/50 w/w S/I) copolymers ranging in molecular weight from 5000 to 20000, as well as several of their blends, are examined by transmission electron microscopy and small-angle neutron scattering. These results are used to interpret toluene gravimetric sorption data collected at various temperatures. At temperatures above the styrenic glass transition temperature, microphase-ordered copolymer melts are found to exhibit Fickian diffusion. In the case of a copolymer with an experimentally accessible ODT, anomalous sorption (as evidenced by equilibrium overshoot in gravimetric mass-uptake curves) is observed at temperatures near, but below, the ODT. Within the disordered state, Fickian diffusion is regained, indicating that the onset of anomalous diffusion is related to a solvent-induced ODT under isothermal conditions.