Tube amp attack sensitivity at home
The short answer to the question, "Can you get tube amp attack sensitivity at relatively low volumes?", is "probably not".
The reason I say that is because I assume that when someone says "relatively low volume" it really means "much quieter than stage volume." Depending upon who you listen to, stage volume can be upwards of 95 dB; modern trends are toward lower volumes to satisfy the sound guy's need to mix everything through the mains. Most guitarists complain about getting "their sound" using a tube amp under those conditions.
When a typical tube amp is working "in the zone", the speaker is pushing about 105 dB at 1M in front of the amp. That's way too loud for typical use in a household where other family members want to be able to hear themselves think while you play. However, the difference between 105 dB and 95 dB is small enough that an attenuator (e.g. Hot Plate) can be used to control the stage volume without significant loss of response. It's still stage, volume, however. Once you start trying to attenuate more than 10 dB or so, the response of the amp suffers; this is why attenuators are not a good solution for playing in a quiet household.
IMO, master volume tube amps don't really cut it, either. You can get distortion at very low volumes (down to conversational levels with no problem), but it's all preamp distortion. Preamp distortion has neither the complexity nor the touch-responsiveness of power-amp distortion. At that point you may as well run a distortion pedal into a turned-down non-master volume tube amp; you get the same effect and you now have a choice of distortion tonality by selecting a pedal that matches your taste.
Believe it or not, a modelling amp is the best solution if you want a cranked-amp tone at household levels. That's what they're designed to do, and while they won't stand up to a good tube amp in a side-by-side comparison at stage volume, they'll certain come out ahead when compared to a tube amp that's throttled back to conversational volume using an attenuator or master volume. FWIW, I believe that the Vox ToneLab is the front-runner when it comes to producing a convincing response to touch in the clean to slightly overdriven range.
All that said (and you'll notice that I assumed you really want to get cranked amp tones at conversational volumes) you may still find a tube amp useful at low playing volumes if you don't need to get enough distortion to play sustained single-note lines. My own playing style is advised more by folk and jazz stylings than rock and blues, and I find the Vibro-King (a 60W amp) to be quite playable at home. I don't expect a lot of distortion for my style. However, the tubes add a wonderful warmth to the clean sound.
I've tried playing through a borrowed Tweed Deluxe (a restored `55 5D3, to be specific) and find that it doesn't have enough headroom for my style, even at family-friendly levels. However, when I crank that amp to get distortion similar to Neil Young's lead sound, it's far too loud for the house.