I’ve done a lot of experimentation with Class A circuits. Class A is an excellent way to smooth the "square waves" from DAC and translate more bass and a more natural sound. I have found that the best number of Class A circuits in an entire audio path is two (meaning from source CD/file all the way to speakers). There was still an excellent amount of quickness, attack, punch and clarity. However, once the audio path contained 3 Class A circuits, I started experiencing the slow down or laid back affect where I would lose resolution/punch in the bass/midbass and the high frequencies definitely started rolling off. Essentially, the sound started becoming a lot warmer/softer/slower. This was not an issue with power supply, as the problem still occurred if I split the Class A circuits between devices (i.e. one Class A in DAC and two in preamp).
If you combine the PS Audio PWD with a BHK, I see three potential circuits that would affect this. One Class A circuit in the DAC, and one Class A circuit + tube gain in the preamp. I suspect the 12AU7 tube stage is going to do something very similar to a Class A stage. This may or may not push your music into the "laid back" area, it highly depends on amplifier, cables, speakers, etc. I can only speak from my personal experience with pieces of equipment.