It's nice to have all this ambiguity in both the versions of the TNG episode, as I, too, would like to believe in NCC-640 in my personal delusionverse. OTOH, there are plenty of other Oberths with five-digit registries (either exactly known or fuzzily glimpsed) to support the idea of ongoing 24th century construction of the type. Or perhaps major reworking, which involves decommissioning and recommissioning.
There are four Oberths with 5XXXX registries:
1. Tsiolkovsky (NCC-640 on the model, NCC-53911 on the dedication plaque), built in 2363.
2. An unnamed Oberth (referred to as the Cochrane in the Encyclopedia) shown on two occasions, with the registry NCC-59318 printed on the model.
3. Biko NCC-50331, although because it's just stock footage of the Cochrane, the 59318 registry can be seen.
4. Pegasus NCC-53847, built in 2358.
While I don't feel like getting into this argument again, I just want to say that I personally feel that having Oberths constructed for 80+ years while at the same time other, more advanced ship classes were being designed and built, is ludicrous. And it's all because of the disconnect between the Art Department and the VFX Department in "The Naked Now" (and partially because the studio was too cheap to construct a new model for the Tsiolkovsky, but at least I can understand their rationale; they didn't want to spend money building new models if the show was going to get cancelled after the first season...which it probably would have if it weren't syndicated).