SQ difference XLR vs RCA ?

no, most likely

My question is this:  if I have a quiet system with short runs, do balanced connections sound better?

They should not sound worse.

As the noise increases, and the runs get longer, the balanced stays better for longer.

Basically:

• If it sounds good now, then do not change it.
• If you are looking at an equipment change, which is more immune to noise, then balanced helps.

No. The difference is incredibly subtle and contingent on your specific components and length of run (if dozens of feet). When you get to own the best system you have ever imagined… then bring this issue up again. For now, rca will do the job and cost less.

RCA and XLR connections can and do sound differently.   I have a Gustard X26 Pro DAC that supports simultaneous RCA and XLR outputs.  I connect them using Harmonic Tech Pro Silway RCA and XLR cables to a PS Audio BHK Preamp which drives a 2A3 tube amp and Tekton Moab speakers.  It is easy to switch inputs to compare the sound of XLR and RCA.  There is a 6 dB difference but that is easy to correct using the volume control of the BHK.  The XLR is brighter and more detailed sounding which is fabulous on classical and many sorts of music but can be a tad fatiguing compared to RCA on tracks that might sound brittle or shrill with that brighter more detailed presentation.  Now I haven't figured out if the difference between XLR and RCA is due to the DAC, the Preamp, or the cables but the fact that it exists is indisputable and would be easily heard by anyone that knows how to listen.  Frankly, I like the fact that I can alter the sonic character so easily by changing the input.

Another factor, some equipment's XLR inputs/outputs are not really truly balanced. The XLR connections were just added for convenience. Unless absolutely necessary I would never use those and would go RCA in that circumstance. This is a question you would need to ask the manufacturer when in doubt.