I have listened to this amp (and looked at it - its s beautiful!). I tried it with Rogers LS2a/2 speakers and with Wilson Audio bookshelf and with Sennheiser HD650s. I think the sound is typical of the amp rather and yes, the amp has a tube quality about it (as compared to solid state at the same price). One great way of hearing the 'sound' of different tubes is to compare the TRV-35SE with its sister the TRV-88SE. The 35 uses EL34 tubes and the KT uses KT88 tubes. The 88 sounds more detailed and has better control of bass but its not quite as engaging/warm. I thought the TRV-88SE was a little boring. I think that the exceptional feature of the 35SE amp is its sound, especially its non fatiguing quality. It is not super energetic but I thought the bass was a little poorly defined sometimes but other reviews have not seemed to notice this. Its not expensive but its not toy prices either and there is plenty of competition at its price. I think it also suffers from boutique pricing and could be cheaper.
I thought the headphone amp was great and I would have been very happy with it. However I ended up buying a Grace Audio m903 as a headphone amp and to use as a preamp. (By the time it arrived I sold the power amp so I have not heard the Grace pre amp function!)
As for the question is this the tube sound? Hard to say. Yes, its a tube amp and yes it is warm and engaging. But in contrast if you listen to the top preamps by ARC I would not describe their sound as tube sound as more like fantastic sound, accurate and detailed. The TRV-35SE does not sound like that - it sounds like itself.
Hope this helps.