An engine system is provided that includes a compressor section, a combustor section, a turbine section, a flowpath and a flow regulator. The combustor section includes a combustion chamber. The flowpath extends sequentially through the compressor section, the combustor section and the turbine section. The flow regulator is configured to open the flowpath between the compressor section and the combustion chamber during a first mode of operation. The flow regulator is configured to at least substantially close the flowpath between the compressor section and the combustion chamber during a second mode of operation.