Does liquid neon retain its properties of lighting up when a charge goes through it the same way it does when it is a gas?

I would say yes, because you're only changing its physical state, rather than reacting the element chemically with another element or compound. Though, I could be wrong, so don't run off and do an experiment just based on what I said.

Density changes radically the process.

 

The orbital energy levels remain nearly the same, BUT:

- The time between two shocks gets tiny, so you won't see any emission lines more. They'll get so broad you can't separate them.

- The distance between two shocks gets tiny, so it needs a much stronger field for an electron or ion to acquire the energy needed to ionize an other atom and maintain the spark.

- The very concentrated spark vaporizes the liquid locally, making the process unstable.

 

In fact, neon discharge tubes use a low pressure to obtain a stable discharge, not just to permit a 100V or 200V spark over a significant distance (only 1/10mm at 1 bar).

 

Sparks in liquids exist and are used, in electrical discharge machining (see Wiki). Very short distance, very destructive.