It may work, and may sound good, even great, but they are different spec tubes.
The 6N3P/5670/2C51/396A tube has the curves/same specs as a 6DJ8/6922/6N23P but a totally different pinout. Therefore, the need for the adapter. Once the adapters are bought, new options are opened for Vali2/Valhalla/Lyr rollers. Because the 6N3P/5670/2C51/396A tubes are rare in audio design, they are cheap on the open market. Further there is no Western Electric option in the 6DJ8/6922/6N23P tube pinout family. The best built tube of all of these are the Western Electric 396A, period. It is just their relative unavailability and high cost make them unsuitable for production quantities.