So, I don't understand much about engineering in general, but since this is a discussion forum, I like to think that this is just a thought exercise (because it is probably useless).
So, the idea would be to use an electric compressor that would pump pressurised air into a combustion chamber without the low pressure fan, and the combustion would happen with traditional jet fuel or other propellants (like pressurised methane?).
The idea is that the pressurised fuel would turn a small electric generator after exiting the fuel tanks, but I doubt that it would generate enough energy to drive the compressor.
Well, it would probably be terrible in subsonic or even supersonic speeds, but maybe it could be also a ramjet/scramjet hybrid (of course, with all the extra equipment it would require to do these functions).