Roughly, potentially, but there are some key differences in the comparison of a jet engine and the theoretical 'electric jet engine', that are very different from the comparison of a car engine to a motor-driven EV.
Most notably, as previously mentioned, is the turbo-fan is mechanically driven by the combustion heat-driven expansion of the air compressed by it's compressor. At cruising speeds (where the jet engine is optimized), this is a much more fuel efficient arrangement than the cruising speed operation of an automobile combustion engine.
Basically, there are two places where the released heat is converted to mechanical energy-- first, much of the heat-release of combustion is captured by the turbine that drives the compressor. Second, the exhaust nozzle also converts heat not captured by the turbine into kinetic energy by accelerating the mass-flow through the engine, converting a pressure delta generated by heat expansion into a velocity delta through nozzle geometry. By comparison, the combustion engine converts the exhaust gas heat expansion into mechanical energy by driving a linear piston, and gains no mechanical energy by exhaust. Generally, turbines are more efficient than pistons at mechanical energy conversion. There's also a tertiary efficiency-- namely that combustion at high pressures more efficiently converts heat to pressure as the gaseous density is higher, so more of the chemical energy of the fuel is converted to kinetic energy in a jet engine than a combustion engine, simply by virtue of the higher pressure of the combustion reaction in the jet engine. The 'downside' for the jet engine is that to make the whole arrangement work fuel efficiently you have to be operating at a significant fraction of Mach, much faster than ground transport can manage safely. Hence, combustion engines rule the earth and jet engines rule the sky in the current paradigm.
So, even assuming unlimited power supply, you would still have to have to have a very efficient motor on an energy cost-efficiency basis. To boot, you would have to have an engine that operated at similar cruise velocities. Even leaving aside infinite power generation, we can still consider that more time in the air is a longer time-frame along which the aircraft must be energy self-sufficient, generally equating to more mass in battery and/or power generation. More mass lowers the mechanical efficiency on an aircraft operation basis, because it is more energy you have to spend to accelerate and decelerate the extra mass.
So in an electric motor driven equivalent, you probably still have something resembling a turbo-fan. Except that your motor is primarily driving your compressor fan, and the turbine is there mostly to recapture some of the energy of compression (which also generates heat) into energy to drive certain engine functions like coolant and lubrication circulation, possibly some power regeneration. So probably a smaller turbine, but this puts you up against the inconvenient fact that compressing air is not very energy efficient as a means of generating thrust. If it were, we'd be running aircraft off compressed air.
What this generically gets at is that the electrification of air travel is likely not to resemble current jet-era technology. It's within the bounds of known technology to apply efficiency of electric motors to the problem of air transport, but the resulting architecture is likely to be very different, much as the fundamental architecture of a full EV is different than a gas automobile. This will likely in addition mean some fundamentally different infrastructure.
E.g. much of the energy of a flight is taken up in the initial acceleration, so it's possible that an Aerial EV would take off from a runway that more resembles that of an aircraft carrier than a flat road, with an assisted launch. Similarly, recapturing the energy on landing could again utilize a system more similar to those seen on aircraft carriers, only dedicated to regenerative capture rather than rapid deceleration.
More directly, though, the fundamental problem is generating thrust at near-Mach speeds. The efficiency of electrical motors at turning electrical power into rotational mechanical power is somewhat mitigated by subsonic and supersonic fluid mechanics, because an aircraft has to generate thrust by accelerating an airflow, or 'pushing' against air in some way or another. At these speeds, propellers basically start to lose their efficiency, and propulsion methods above these speeds therefore rely on the expansion of gasses with the transfer of heat into the gas. So to compete in these speed areas, an energy efficient means of transferring heat to (compressed) airflow has to be devised, which is very different than simply applying known electric motor technology.
