Initial states in incompressible two-dimensional magnetohydrodynamics that are known to lead to strong current sheets and (laminar) magnetic reconnection are modified by the addition of small-scale turbulent perturbations of various energies. The evolution of these states is computed with the aim of ascertaining the influence of the turbulence on the underlying laminar solution. Two main questions are addressed here: (1) What effect does small-scale turbulence have on the energy dissipation rate of the underlying solution? (2) What is the threshold turbulent perturbation level above which the original laminar reconnective dynamics is no longer recognizable. The simulations show that while the laminar dynamics persist the dissipation rates are largely unaffected by the turbulence, other than modest increases attributable to the additional small length scales present in the new initial condition. The solutions themselves are also remarkably insensitive to small-scale turbulent perturbations unless the perturbations are large enough to undermine the integrity of the underlying cellular flow pattern. Indeed, even initial states that lead to the evolution of small-scale microscopic sheets can survive the addition of modest turbulence. The role of a large-scale organizing background magnetic field is also addressed.