We explore the possibility that GSC 07396–00759 (spectral type M1e) is a widely separated (∼282, or projected separation ∼12,350 AU) companion to the "old" (age ∼12 Myr) classical T Tauri binary system V4046 Sgr AB, as suggested by the proximity and similar space motions of the two systems. If the two systems are equidistant and coeval, then GSC 07396–00759, like V4046 Sgr AB, must be a spectroscopic binary with nearly equal-mass components, and V4046 Sgr must be at least ∼8 Myr old. Analysis of a serendipitous Chandra X-ray grating spectrum and light curve as well as XMM-Newton light curves and CCD spectra of GSC 07396–00759 obtained during long exposures targeting V4046 Sgr AB reveals a relatively hard (T_X ∼ 10⁷ K) X-ray spectrum, strong flaring, and relatively low-density plasma. These X-ray characteristics of GCS 07396–00759 are indicative of a high level of coronal activity, consistent with its apparent weak-lined T Tauri star status. Interactions between V4046 Sgr AB and GCS 07396–00759 when the two systems were more closely bound may be responsible for (1) their dissolution ∼10⁶ yr ago, (2) the present tight, circular orbit of V4046 Sgr AB, and (3) the persistence of the gaseous circumbinary disk still orbiting V4046 Sgr AB.