A lot of people think the glow plugs in model engines are just like the ones used in large Diesels engines (i.e. trucks). They are not the same. In a Diesel, the glow plug is energized when the engine is cold to pre-heat the combustion chamber for easy starting. After that, it is shut off and plays no role. In a glow model engine, things are different. There is generally a coating of platinum on the heating coil. The battery gets the coil hot initially for starting but the coils stays glowing after that. The platinum acts like a catalyst, just like it does in the catalytic converter on your car. This promotes fuel burn which creates heat and keeps the coil glowing red hot the entire time that the engine is running. This makes a model engine a "glow ignition" engine rather than "compression ignition" (Diesel) or "spark cognition" (gasoline).

So to answer your question, yes the glow plug plays a huge role while in flight. They can fail in two ways:

The first is a burnt open coil. You usually discover this when connecting the battery and trying to start the engine. The coil just won't glow and the engine won't start.

The second is a degraded or contaminated coil. There is still a metal coil there so it will glow with the battery connected and the engine may start. As soon as the battery is gone though, it can't sustain the catalytic reaction very well. This results in misfires and poor running just like a bad spark plug in your car would. You may very well notice this in flight as a really noticeable problem or maybe the engine just doesn't seem "right".