Turning chemical energy (low entropy energy) into electrical energy (low-medium entropy) into thermal energy (high entropy) to make mechanical energy (of intermediate) would be incredibly inefficient. Combustible fuels are much better than batteries at making things hot; I don't have the time to run the numbers right now, but what you are saying is incredibly wasteful. Please take a thermodynamics course.
Fans are commonly used on supersonic aircraft. Most modern fighter aircraft use medium or low bypass turbofans, which are using fans to go supersonic. Turbofans are less efficient than turbojets over Mach ~1.6-1.8 (or in reheat), but a ducted fan could probably do better.