Rare or not??

[CtCarGuy]

I just saw a 1956 T'Bird with less than 7000 documented miles and probably would be considered a "survivor". The interior and trunk are like new. The body has the typical lacquer chips/crazing. The paint measures 4-9mm which I think is all original. Other than the wrong hose clamps, it looks fine. It does run and drive just fine. So the questions are:
Can this be the (or one of) the lowest mileage 56's in the country?
Would it being an all original example add value?

I am looking at this as an investment, not to restore or use much (maybe 100 miles year). I already have a 56 that I love to drive. I did some looking and all of the "low" mileage cars for sale have been restored and in many (if not all) had the odometer set back to 0 after restoration (even though I don't think that is legal).

Thanks

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[CtCarGuy]

UPDATE:
After spending several hours examining the car, here is what I found:
Manf, April 1955
Paint original except for left rear and driver door.
Paint is enamel
Seat was replaced
Door panels replaced
Dashpad pliable
Re-manufactured power brake booster
Wrong radiator hoses and clamps.
Heater hoses disconnected
Rot on left front lower quarter (inside)
New brake hoses
Some new suspension parts
New exhaust
Damage to rear valance
Soft top is black and pliable.
The only proof of mileage is title

Result is this is a restorable but NOT rare car but that is all. The mileage is undocumented and there are just too many items replaced that a 6000 mile car should not need.

 

[Rich's 56]

UPDATE:
After spending several hours examining the car, here is what I found:
Manf, April 1955
Paint original except for left rear and driver door.
Paint is enamel
Seat was replaced
Door panels replaced
Dashpad pliable
Re-manufactured power brake booster
Wrong radiator hoses and clamps.
Heater hoses disconnected
Rot on left front lower quarter (inside)
New brake hoses
Some new suspension parts
New exhaust
Damage to rear valance
Soft top is black and pliable.
The only proof of mileage is title

Result is this is a restorable but NOT rare car but that is all. The mileage is undocumented and there are just too many items replaced that a 6000 mile car should not need.

 

[Rich's 56]

sounds like the odometer has rolled over.