Does preheating fuel before it reaches the turbine result in a performance improvement?
The key here is understanding the purpose of pre-heating. Combustion occurs very rapidly to produce the power stroke in piston engines and thrust in jets.
It's time in the combustion chamber to do so is measured in fractions of a second.

Ideally, a mixture of 2 gasses, methane and air for example, would ensure efficient and complete combustion.  This is your common kitchen stove.

Mixing liquids with air is more problematic, as now you have a mist of small droplets instead of ready to mix gas.  This is good and bad.  The good is the evaporation of the fuel helps keep the engine cooler. This is a benefit of "full rich" setting.  The bad is the fuel is not mixed as well with the air when it burns, lowering efficiency and releasing harmful byproducts such as carbon monoxide.

Proper design (operating temperature) and choice of fuel may eliminate the need for pre-heating, especially once the engine is "warmed up". 

Aside from the dangers of heating fuel, gains may be made by standardizing the temperature of fuel inflow for pollution control. Another possibility is to use the heat from turbo compressed air to warm it.  Tight control of octane rating is also beneficial.

But aircraft operators adjust their richness based on RPM and usually on the rich side to avoid overheating the engine, which is far more disastrous than slightly lower fuel milage.

In design, using engine heat to evaporate the fuel may eliminate the need for pre-heating, except for extreme arctic applications.