In the ocean, NO3 and PO4 is around the level of 0.00x ppm, or x ppb, and corals still thrive.
Besides even if you have no measurable NO3/PO4 in your aquarium there'll always be enough dissolved organics that NO3/PO4 are created continuously and that'd be more than enough for your corals to sustain.
For SPS tanks, if you've more than 1-2 ppm NO3, SPS will tend to brown out very easily, that's why we normally aim at zero (non-measurable) NO3/PO4.
So answering your question, NO3 = more growth? Perhaps - my SPS's are growing pretty fast in my tank with non-measurable NO3/PO4, but even if having NO3 will make them grow faster, you'll most likely ended up with a faster growing piece of brown sticks.