I've heard that turbines can use a variety of fuels, but gasoline doesn't seem like it would be suitable. I know marine and power generation turbines can be pretty tolerant of different fuels, and they're really just jet engines. But I haven't heard of anything used that isn't close to kerosene. The US Navy previously considered using JP-5 jet fuel for their marine turbines, which would be a common fuel for their helicopters. Power generation turbines typically use natural gas, but that obviously requires a way to feed it. I see this list has a lot of things including some gasoline components, but it doesn't include gasoline or diesel.
GE Gas Power's variety of fuels
- Arabian Extra Light Crude Oil (AXL)
- Arabian Super Light (ASL)
- Biodiesel Condensate or Natural Gas Liquids (NGL)
- Dimethyl Ether (DME)
- Distillate Oil #2 (DO2)
- Ethane (C2)
- Heavy Crude Oil
- Heavy Fuel Oil (HFO)
- High H2
- Hydrogen Blends
- Kerosene (Jet A or Jet A-1)
- Lean Methane
- Light Crude Oil (LCO)
- Liquid Natural Gas (LNG)
- Liquefied Propane Gas (LPG)
- Medium Crude Oil
- Methanol / Ethanol (Alcohol)
- Naphtha
- Natural Gas (NG)
- Sour Gas (H2S)
- Steel Mill Gases
- Syngas
There was an episode of The A-Team where Murdock has to land a helicopter that's low on fuel at a gas station and then fills it at a gas pump. Looks like a Bell Jet Ranger, which I'm pretty sure is powered by a turboshaft requiring jet fuel.
Still - not sure about gasoline.