The whole NAD silverline is zero negative feedback.

I doubt that... at least, not as it's written there.

They may very well have no _global_ negative feedback.

They almost certainly have _local_ negative feedback, in each
individual stage. You need at least some local feedback in order to
make each stage (e.g. input, driver, output) linear enough to deliver
acceptable performance. Local feedback may be something as simple as
an emitter or source resistor.

Yup... I just checked their brochure, and they state that (e.g.)
"[T]he S300's amplifier circuits avoid overall ('global') negative
feedback altogether."

Question: Is negative feedback a big deal or not?

Depends on what kind, how you use it, and other details of the circuit.

In general, in order to get either a tube or transistor (bipolar or
MOSFET) to amplify without distortion, you need at least _some_
feedback in order to linearize the device's behavior. The feedback
may be local (e.g. the output of the device is somehow fed back to the
device's input, with appropriate phase inversion), or it may "reach
back" to the beginning of an earlier stage in the amplifier (this is
often referred to as "global" negative feedback).

If you have no negative feedback at all, you're going to be very
limited in both the distortion level you can achieve, and the amount
of power you can deliver.

Some designers prefer to use only local (single-stage) feedback - in
effect, making each stage of the amplifier acceptably linear
(low-enough distortion), and accepting that the remaining distortions
are going to add up. This appears to be what NAD has done in the
Silver series.

Some designers prefer to use both local feedback, and some amount of
global feedback. Done well, this can lower the total distortion
level. Done badly, it can cause problems... in particular, "ringing"
or other forms of instability. [The cause of these stability problems
has been known for decades, and designers really shouldn't be making
this sort of mistake today, but it's always possible...]

Some designers prefer to use only local feedback to reduce distortion
in the audio spectrum, but to include a low-speed global feedback loop
to "null out" any DC offset created by any of the stages in the amp.

I believe it's possible to produce excellent, audibly-transparent
amplifiers with any of these approaches. It's also possible to yngvi
up a design which uses any of these, and generate various sorts of
distortion (some of which may be euphonic, and some of which may sound
downright nasty).

I once had a chance
to compare 2 similar tube amps built by a local tube tweek in Holland,
One was with some kind of config with a bit of negative feedback, and
the other with absolutely none. The result: I really felt the one with
no negative feedback was more detailed. (I was blinded later when I
really wanted to know) The amps were identical outside and in. I could
discern the difference reliably not only because of the detail, but
also the bass sounded tighter with the neg feedback. But the clarity
was noticable.

This might indicate more accuracy in the amp without global feedback,
or it might indicate that the amp without global feedback was actually
introducing a slight high-frequency boost for some reason. Impossible
to tell from your description, I'm afraid.