We present the first detailed imaging polarization observations of six SMC and six LMC clusters, known to have large populations of B-type stars that exhibit excess Hα emission from 2-CD photometric studies, to constrain the evolutionary status of these stars and hence better establish links between the onset of disk formation in classical Be stars and cluster age and/or metallicity. We parameterize and remove the interstellar polarization (ISP) associated with each line of sight, thereby isolating the presence of any intrinsic polarization. We use the wavelength dependence of this intrinsic polarization to discriminate pure gas disk systems, i.e., classical Be stars, from composite gas-plus-dust disk systems, i.e., Herbig Ae/Be or B[e] stars. Our intrinsic polarization results, along with available near-IR color information, support the suggestion of Wisniewski et al. that classical Be stars are present in clusters of age 5-8 Myr and contradict assertions that the Be phenomenon only develops in the second half of a B star's main-sequence lifetime, i.e., no earlier than 10 Myr. The prevalence of polarimetric Balmer jump signatures decreases with metallicity; we speculate that either it is more difficult to form large disk systems in low-metallicity environments or that average disk temperatures are higher in low-metallicity environments. The polarimetric signatures of ~25% of our sample appear unlikely to arise from true classical Be star disk systems, suggesting one should proceed with caution when attempting to determine the role of evolutionary age and/or metallicity in the Be phenomenon purely via 2-CD results.