During the close approach of two galaxies in a merger, tidally induced gas inflows can trigger simultaneous black hole accretion which are observed as dual active galactic nuclei (dAGNs). Merger simulations predict that the resulting increased nuclear gas reservoirs will obscure the X-ray emissions from the AGNs. We investigate whether dAGNs in mergers are observed to be more obscured than their isolated counterparts by combining the results of previous radio and optical spectroscopy studies with new Chandra X-ray observations for a sample of 4 dAGN systems in the Stripe 82 field. For the 6 detected components, we find the rest-frame X-ray luminosities range between 39.8 < log LX /erg s-1 < 42.0. The sources have redshifts between 0.04 < z < 0.22 and projected separations between 4.3 and 9.2 kpc, as well as multi-wavelength properties most closely resembling low-luminosity AGNs. However, we determine that the X-ray emissions for 2 of the sources likely has strong contributions from hot interstellar medium, and star-formation and X-ray binaries may contribute to the X-ray luminosities of several sources. We do not find evidence of enhanced obscuration through our analysis of X-ray hardness ratios, optical [O III] emission line luminosities, and mid-infrared luminosities. Therefore, we suggest that the unobscured low-level accretion observed for the AGNs in this sample is driven through stochastic processes rather than the massive gas inflows predicted for a merger-driven scenario.