The ground can range from a coat of glue (rarely done in antiquity.  This turns black after about a hundred years and is easy to spot.) to white or some very colorful ones of yellow or red.  Yellow is the more common color of the latter group.

The purpose of the ground is two-fold.  First, it is thick enough to fill and cover flaws in the underlying wood.  This gives an even surface, both in texture and patina, to then receive the varnish.

Second, because the ground is made of PARTICLES, these reflect light as it passes through the varnish before it hits the wood and then again as the light is reflected off of the wood surface.  This in turn gives the varnish a brilliant appearance.  I am not sure why ground is given the little attention it receives.  Clearly, the ground effects the appearance far more than the varnish does. This is because the ground is designed to let light pass through, but adds thousands of "little reflectors" in the process.  The effect this has on both the wood and the color in the varnish can be astonishing. This concept we see in paint used in street signs.  Originally, street signs were painted with tiny bits of glass in the paint (today they use something similar.  I am not sure if it is glass though!)  The glass would then reflect the headlights and make the sign "jump out" to the night driver. 

Varnish with a good ground "jumps out" also.  The instrument has an appearance that can never be duplicated by varnish alone, no matter the quality of varnish used.

When it comes to appearance, this use of ground, I think anyway, sets the master apart from the common maker.  It is the difference between a Rembrandt and good furniture; that is, a beautiful ground makes the VIOLIN "jump out" at you, beautiful varnish alone makes the WOOD "jump out" at you.  If I want the wood to jump out, I will buy some really nice paneling for my living room instead!

One side note, because the ground and varnish add weight to the fiddle, the wood must be adjusted to accomodate them BEFORE their application.  If a fiddle sounds good in the white (without varnish), the varnish will almost certainly destroy the tone.  This is because varnish is mass or weight burdening the instrument.

The way to overcome this is to remove the equivalent amount of wood mass as varnish mass will add.  In other words, once a fiddle sounds good in the white, the back and top must be slightly thinned until they actually give a slight metallic sound to the fiddle.  Once the varnish is added, the metallic sound disappears and the beautiful tone is restored.  If this is not done, and a good sounding white fiddle is varnished, the result is a heavy tone, or "masculine" tone that will not be very inviting.  If this has already happened, the fiddle must be opened up and the removal done from the inside.

Best wishes

The short answer is that it does not effect the value if varnish has been added, as a rule.  The value is greatly impacted if the original varnish was intentionally removed before the revarnishing of the instrument, however.  If, though, the original varnish over time was simply worn away, this is so common as to be expected. New varnish, properly applied, over this will not devalue the instrument, generally. 

Virtually all the old masters' instruments have little original varnish left.  This is particularly true in areas of the instrument that have come under alot of human contact. An exception would be a fiddle such as the Strad Messiah, but again, I doubt this Strad was ever played much.

Restoration of instruments took a different turn in the twentieth century.  In earlier times, the fiddle was played and when the varnish was worn down badly, the next time it was repaired, the luthier added more varnish to simply bring it back to what it was.  Thus, wear was acceptable.  Even today, a fiddle that has a very good wear pattern, wear on the top near the fingerboard, lower bass bout, etc., will attract alot of attention.  The observer's reasoning is that the instrument was played alot by a real fiddler.  Therefore, they conclude, it must sound pretty good.  This kind of wear can increase the value, particularly in the lower-end value instruments.

The restoration approach in modern times leans toward restoration and preservation as opposed to simply repair.  Thus, very few high dollar instruments are preserved in such a way as to permit the fiddler to actually come in contact with the original varnish.  Instead, a fine layer of varnish (and sometimes not so fine) is put over the original.  This keeps the wear to the original varnish at nearly zero percent. 

Your question about remedial treatment of varnish appears to me to be this:  "Can varnish be removed to restore the instrument to the original varnish?"

Yes.  Generally, there are two types of original varnish a luthier will find on an instrument.  Oil based and alcohal based (usually called spirit varnish).  Most old instruments used oil.  Alot of moderns used spirit.  If anything else was used, such as cellulose-base, etc., the fiddle almost certainly is of little value as it was a mass production, and anything done to it won't matter anyway.

There generally are only two original types, but in modern times there are MANY types that can be put on top of these.  Amateurs generally choose some of these.  Polyurethane, for example (yikes!).

Generally, luthiers choose one of three methods of varnish protection. 

1) Oil on top of oil. In this method, the new varnish essentially grafts to the old.  This is chosen oftentimes when wear to the original is very bad.  The repair in this instance is virtually permanent.  It still can be removed, however.  The only way to do so, requires alot of labor.  It essentially must be removed by a LOT of hand rubbing with abrasives.  If the match was good, it is essentially impossible to tell what is original and what isn't.  One can see the difficulties that may arise from this approach. 

2) Spirit on top of oil or spirit.  For oil varnish protection, spirit varnish is the best way.  The reason is that the spirit varnish can at any time be removed with alcohal and the oil based original left intact.  Spirit on top of spirit grafts to the original even better than oil on oil.  This can create problems, if done excessively, as the new varnish, if it is to be removed in the future, must be removed with a lot of hand rubbing with abrasives.  The best way I have found to repair spirit based is to clean the varnish with xylene.  Touch up the wear or chipped areas with watercolor. Then simply apply new spirit varnish where I want match a repair or replace damaged varnish.  I then french polish the area I want protected instead of varnishing it.

3) French polish.  This is done alot by luthiers.  (French polish is what gives shine to the bare wood of the neck.) The advantage is that the polish is extremely thin, and as a rule does not alter the soft shine of the original varnish.  It still affords protection and can be done routinely.  Some skeptics scoff at this approach.  But trust me, MANY luthiers find this the best way to blend abnormalities in the varnish and afford a quick fix that actually is very, very good.

Hope this answers the question.