First, there is no definition of what 9.975 really is. Even if you went by the technical manuals (which is pointless), they would still say less than the 21,000 that you say.
Second, while a velocity might be sustainable, that does not make it efficient. With a scarcity of resources, they would be unlikely to sustain such speeds.
Third, they would definitely need to make stops to attain resources. It is unlikely that such a ship could ever be meant to make a voyage meant to last even a few years without refueling.