To facilitate the integration of a rotating detonation combustor (RDC) in a turbomachine, adding an ejector downstream of the combustor may be a viable option. The present work examines the performance of an ejector configuration under unsteady inflow conditions representative of an RDC exhaust, using a Large-Eddy Simulation. The RDC exhaust gas is generated at the nozzle exit of the ejector by an adequate choice of inlet axial fluctuation amplitude and frequency. The results along the jet centerline showed that the ejector flow remains in the low supersonic regime before passing through a secondary shock located at the constant-area mixing chamber exit. Mixing between the two flows begins immediately at the confluence and terminates slightly upstream of the secondary shock. The consideration of a theoretical thermodynamic cycle with the calculated ejector revealed that the ejector presence increases specific fuel consumption with respect to a reference cycle without an ejector installed. Entropy generation analysis showed that losses associated with thermal conduction have the most significant impact, followed by viscous dissipation losses. Both originate primarily in the shear layer between the RDC exhaust and the secondary flow. The flow characteristics at the ejector outlet and turbine inlet underline the potential of the ejector to couple the RDC with an axial turbine. Total pressure fluctuations are dampened by 65%, whereas the Mach number and the total temperature distortion are reduced to acceptable levels.