Yes, I use it to protect permanent connections like set-screw, crimp, solder... although the connection is gas-tight I want to protect the wire going from the connection to the wire, even if this is kept to a minimum length of a mm or so it's still unprotected wire which will corrode over time.
Some of Furutech's power cables, like the FP-S55N, use the nano-liquid in the stranding of the PC and the PCs that use this liquid perform at a much higher level than you might expect from the basic design and materials used so I do think the Nano-liquid is legit, and I also have had nothing but good experiences with Furutech products, they are very good quality and imo you can trust their claims. Disclaimer: I am a Furutech dealer and use their products to make my many of my cables.
I first clean all connections with MG Chems Flux Remover and a soft brush (toothbrush works), then add the Nano Liquid or Caig ProGold 100% brush-on formula to plated connections.
I have found that accumulation of contaminants on plated surfaces can be more of an issue for ground connections, especially if there are any ground loops present. Plated connections can accumulate contaminants just sitting there because of the current flow, so they really should be cleaned every 6 months or so just as a routine maintenance precaution.