No, it's not a law in the same way as physical laws. Most of the failures in economics of the past 50 years can be mostly directly attributed to a fatal overcommitment to the belief that these attributed relations are incontrivertible.

What really exists, closest to the limit we will call "hard science" or "physics", is the microcosmic focus on individuals interacting in a market. Everything else -- supply and demand as a theory definitely included -- is a statistical extrapolation from micro-scale interactions. Hence the label of "dismal science". It's dismal because every hardline assumption is inevitably contravened by real life physics.