High-power electron beams are sought-after tools in support to a wide array of societal applications. This paper investigates the production of high-power electron beams by combining a high-current field-emission electron source to a superconducting radio-frequency (SRF) cavity. We especially carry out beam-dynamics simulations that demonstrate the viability of the scheme to form $sim$ 300 kW average-power electron beam using a 1+1/2-cell SRF gun.