The short answer is, yes, Aerith's fate in Rebirth is the same as it was in the original Final Fantasy 7. However, there's a much longer answer that surrounds that, as Rebirth adds a ton of new details to the event, and introduces a whole slew of new questions and ideas, including a multiverse.
The dream date sequence serves a couple of purposes but primarily is used to get a new White Materia for Cloud to take back to the main universe. Before we go on, it's important to note that there's a lot of ambiguity in the final hours of Final Fantasy 7 Rebirth, and without knowing where the story goes in the next part, a lot of it is up to interpretation.
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