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I mean "unresolvable" in the same sense that two nearby point sources through a diffraction-limited lens are unresolvable. If you watch the video, it appears as if there is only one wavefunction for the BEC of many particles (presuming that is what the video is depicting). Is that in any way an accurate depiction of what's going on?

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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).

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