Determining the initial stellar multiplicity is a challenging problem since protostars are faint and deeply embedded at early times; once formed, multiple protostellar systems may significantly dynamically evolve before they are optically revealed. Interferometers such as Combined Array for Research in Millimeter-wave Astronomy (CARMA) and Atacama Large Millimeter/submillimeter Array (ALMA) make it possible to probe the scales at which turbulent fragmentation occurs in dust continuum emission, potentially constraining early stellar multiplicity. In this Letter, we present synthetic observations of starless and protostellar cores undergoing fragmentation on scales of a few thousand astronomical units to produce wide binary systems. We show that interferometric observations of starless cores by CARMA should be predominantly featureless at early stages, although wide protostellar companions should be apparent. The enhanced capabilities of ALMA improve the detection of core morphology so that it may be possible to detect substructure at earlier times. In either case, spatial filtering from interferometry reduces the observed core substructure and often eradicates traces of existing filamentary morphology on scales down to 0.025 pc. However, some missing structure may be recaptured by combining data from the ALMA full science and Atacama compact arrays.