Well, yes and no. An impulse is really defined within the digital domain to mean a signal with 0 for all time except at one moment where the value is non-zero. This signal has the property that it contains an equal amount of all frequencies up to the Nyquist frequency (which is defined by 1/2 the sample rate). So the digital signal has a very well defined meaning, and does not have infinite bandwidth. The above mention of the sinc function is actually the correct continuous domain representation of how the voltage should change to represent such a signal when passed through a DAC. It's actually so fundamental that it's really the *only* measurement that you need to obtain from a DAC to see how it performs (weird isn't it?).
Here's an impulse in the digital domain with the expected output overlayed:
The dots represent the samples, the blue line is the expected output voltage from the DAC which would be generated for such an input. The curve passes through all the zero sample before and after the non-zero sample, but wobbles above and below the zero line.
Now you've probably heard of different reconstruction filters, and there are choices other than sinc, they are basically the same function but with the phase non-linear, with the 'benefit' of changing the amount of pre-ringing.
For example, the above impulse sent out the headphone socket on my macbook and captured on an oscilloscope looks like:
Which is definitely not the sinc function we see above! However, we can see much more ringing after the impulse, it's almost as if the energy has to come out somewhere isn't it?
If we zoom in on this tail and stick some cursors on, we can see the sample rate showing this is basically doing the same frequency 'wobble' as above:
You can tell from this that my sample rate is 44.1Khz, measurement imprecision withstanding.
Does this kind of help or am I just causing more confusion?
Take away - an impulse gives some sort of nyquist frequency ringing in the output, which can be pre or post the event. It's not a bug, it's correct (well, the above is not correct, that's a modified response in order to make the implementation easier, probably some sort of IIR filter but we're getting far off point to cover that sort of thing).
If I were to overlay the frequency response of the impulse, it would be essentially flat out to Nyquist. The difference in the above plot vs the pre-ringing one would be visible in a phase shift across the frequencies, not the amplitudes. So, if you think that phase should be preserved at all costs, you want a DAC with pre-ringing. If you think that pre-ringing is the work of the devil, you end up with phase inaccuracies. Trading one off against the other to produce a pretty picture is left as an exercise for the reader.
P.S I can't hear the difference between different filter types, and if pre-ringing was so terrible it would be obvious right? It's not clear what the chord filter response is, it could be either of these, or something in between. The fact they talk in their marketing about some special filter would suggest it's not straight sinc, but it won't be far off.