Not once it's running, vs. magnetos and plugs on the gas engine.
Gasoline powered piston aircraft typically have multiple electric systems.
The "airframe" electrical system (possibly one of several) includes alternators or generators, batteries, electric items like radios, lights, ice protection, and electric fuel boost pumps, and the engine starter. This can all be shut off with a master switch independent of propulsion. If you turn the key to start the engine with the master off, the starter won't crank, but you'll look like an idiot.
The "propulsion" electrical system includes the mags and plugs. You can actually shut off the master electrics off in flight with no effect on a manually controlled engine. It'll keep cranking along, and you can still operate the throttle(s) mixture, and carb heat controls. There are usually two magnetos powering one plug in each cylinder for two plugs per. This is actually for performance reasons, not reliability. Running the engine on one of the two magnetos will result in ~75-125 RPM drop. This doesn't sound significant to car guys, but it can make a difference during level flight near max gross weight and a big one during climb.
I'd put glow plugs and starters on a diesel into the "airframe" category, because it's no longer needed once the engine starts. The diesel powered craft that Frank mentioned in regards to a crash had FADEC, Full Authority Digital Engine Control, which allows a computer to maintain mixture and other engine settings (kinda' like a modern car), and facilitates throttle control with an autopilot. When FADEC fails hard, so often does the propulsion, but this isn't a diesel only issue, as it can happen with gasoline pistons or turbines that employ it.
In reliability speak, failing to start is very minor compared to failing in flight, as it's easier to "not fly" if you're already on the ground. The guys in the crash jump started a dead twin-engine airplane only to have the airframe electrics quit in flight, taking the digitally controlled engines out as well.