If the EPU (Emergency Power Unit) on a modern fighter jet fails, will the aircraft drop out of the sky?
How Are Modern Fighter Aircraft Controlled?

The F16 was the first US military aircraft to be designed around the revolutionary fly-by-wire concept.  This meant there were no direct mechanical linkages between the cockpit and major control surfaces, and that all pilot input was electronically carried to the hydraulic system via wire.  However, since the F16 burst into the scene, there have been further major advancements in aircraft systems design.  Late Gen 4 aircraft, such as the F/A 18 Super Hornet, are designed around a concept now called control-by-wire.  Control-by-wire aircraft not only have removed mechanical linkages to the hydraulic system, but now the pilot is only a voting member.  This means that all input is received by a computer bank that then computes what it thinks the pilot is intending to do, and then autonomously operates the control surfaces to achieve the effect.  This means that Gen 4 aircraft rely heavily on both computer integrity (and there are plenty of self-healing backups), and the power required to run those systems.

Power Failure

If there was a catastrophic total electrical failure and the only remaining power supply was the battery, the only option is for the pilot to restart a generator.  In the event that the engines were operating and all power generation was destroyed, the aircraft would only be flyable for the duration which the battery could provide power to the aircraft--that's a very limited duration.  

Possible other scenarios could include a dual-engine failure. In this instance, the aircraft may be able to fly fast enough to generate enough airflow down the turbine to turn the generator and perform an airstart, but this would only be useful in a dual engine failure, and only if there was enough altitude and airspeed to trade to make it a realistic option.  Otherwise, the battery would probably be used to power the APU, and attempt a relight.  Again, if both engines relit and the generators (including the APU) failed to produce power, then the aircraft would not be flyable.

But what about the RAT?

Although currently in limited use on some trainer aircraft like the T-45, modern fighter aircraft do not use a RAT.

So what usually happens in a total electrical failure?

If the aircrew cannot get a generator back online then they eject.