Embodiments of a Gas Turbine Engine (“GTE”) are provided, as are embodiments of a plasma flow-controlled intake system for deployment on a GTE. In one embodiment, the GTE includes a turbine section, a combustion section upstream of the turbine section, a compressor section upstream of the combustion section, and intake section upstream of the compressor section. The intake section includes a plenum, a first inlet fluidly coupled to the plenum, and a flow-obstructing structure projecting into the plenum and having an outer surface impinged by the airflow directed into the plenum through the first inlet during operation of the GTE. A first array of plasma actuators is disposed on flow-obstructing structure and, when activated, suppresses vortex shedding of the air flowing over the outer surface of the flow-obstructing structure.