Upon their formation, dynamically cool (collapsing) star clusters will, within only a few million years, achieve stellar mass segregation for stars down to a few solar masses, simply because of gravitational two-body encounters. Since binary systems are, on average, more massive than single stars, one would expect them to also rapidly mass segregate dynamically. Contrary to these expectations and based on high-resolution Hubble Space Telescope observations, we show that the compact, 15-30 Myr-old Large Magellanic Cloud cluster NGC 1818 exhibits tantalizing hints at the >= 2 sigma level of significance (> 3 sigma if we assume a power-law secondary-to-primary mass-ratio distribution) of an increasing fraction of F-star binary systems (with combined masses of 1.3-1.6 Msun) with increasing distance from the cluster center, specifically between the inner 10 to 20 (approximately equivalent to the clusters core and half-mass radii) and the outer 60 to 80. If confirmed, this will offer support of the theoretically predicted but thus far unobserved dynamical disruption processes of the significant population of soft binary systems---with relatively low binding energies compared to the kinetic energy of their stellar members---in star clusters, which we have access to here by virtue of the clusters unique combination of youth and high stellar density.