Can you run low voltage current through galvanized steel suspension cable?
"Sí, se puede"

This should be fine. Some years ago there was trendy lighting that used suspended cables with 24VAC low-voltage bulbs; what you're doing is similar. I suggest this as this could be a source for some of the bits and pieces you might need, even if you don't use their special super-duper expensive stranded cable.

(My suggestion? IKEA makes those 'DIGNITET' cable curtain rods. If you have one laying around unused, that could totally work for suspending a low-voltage wire from a ceiling.)

Safety-wise, it's low-voltage (less than 50VAC) and generally 'touch-safe' based on SELV limits. Since it's indoors, even better.

So... go forth and be your bad self and hang that LED bar.