As has already been said, you can't bypass the Hugo₂'s headphone «amp», since it is identical to its line-out stage. Which in fact is also an amp in the wider sense, but one that is present in every DAC, even those without a headphone output. This combined function is its great strength, as it enables to connect headphones directly with the DAC – so to speak –, without an extra gain stage, thus sacrificing as little transparency and accuracy as possible. The term «double amping» is justified nonetheless, since you'd add a useless amplification stage. Although you could just as well renounce it. Either way, adding a headphone amp technically only makes sense if you want to use extremely insensitive headphones.
With the Qutest you have no choice. It's not just that it doesn't have the (lossless) digital volume control, its otput stage also isn't suitable for driving headphones (initially I wrongly thought it was identical to the Hugo₂'s), otherwise it would have left the possibility to regulate the volume via software beforehand, although not losslessly.
Pairing the Hugo₂ with an external headphone amplifier does in no way affect the sound quality any more than with any other DAC. And the difference to DACs with integrated headphone amp is just that you don't bypass an allegedly inferior amp and replace it with a better one, instead you amplify the signal a second time: the original «inferior» headphone amp is still in the signal path.
So using a tube amp with the Hugo₂ will probably offer you what you expect from it: a sound that's spiced up, richer and warmer than the direct connection. I understand that not everyone is as interested in preserved transparency as I am, but adding an amp to a DAC with the best integrated headphone amp you can get – a wire without gain – is a strategy with an extremely poor price/performance ratio. $1000, $2000, $3000 for a one-trick effect device. You'd be better off with one of the various (tube-)amp emulator programs, some of them are even free, and all of them offer the possibility to adjust various parameters. They would still offer the main function of such an approach: masking the tonal flaws within a system, mainly from the sound transducers.
Well, you could do even better – if you want to maximize transparency and accuracy (high fidelity) as well as listening pleasure, use a good software equalizer and linearize your headphones! It would make any masking effects obsolete, so you could enjoy the music in its full detail and transparency. You can still adjust the tonal balance to your individual HRTF and to your personal sonic ideal – without sacrificing transparency. Note that a perfect linearization of the over-all amplitude response also results in a perfect impulse response, which clearly pays off.
The above is also dedicated to my friend
Hooster.
As good as the Qutest is as a DAC, especially considering its price, in my book it is the least attractive offering within the Chord lineup:
No (lossless) digital volume regulation: You need an integrated amp for a speaker system. Or, if you're lucky, you have a power amp with volume control. Otherwise you have to buy a preamp. To achieve (almost) the same signal integrity as from the Hugo₂ with a preamp, you'd have to invest $875,000.
No crossfeed: which prevents it from offering optimal results with speaker-based recordings through headphones.
No headphone output: You need a separate headphone amp. To achieve (almost) the same signal integrity as from the Hugo₂ you would again have to invest $985,000.