Indeed, that's accurate (apart from finite temperature and interaction effects). A BEC is in some ways pretty similar to a laser, where all the photons are in the same state, even quantum mechanically.

But it's important to distinguish between a BEC and a superfluid. Superfluids are the substances with strange collective properties, and these properties come from being cold, bosonic, and interacting. BECs with very low inter-particle interactions do not behave like superfluids, but will exhibit e.g. interference (just like a laser, which is kinda like a non-interacting BEC).