I have seen them do so, though if it was grafted on disease-resistant rootstock, it won't be the same as the original.

It will die if it is a 100% transection. The inability for the vine to transport sugar back down to the roots will cause it to die. Sort of the same thing happens when a tree is girdled.

Unlike olives, and many fruits related to roses, grapes do not produce adventitious shoots from the roots. On the other hand, grapes are normally reproduced by long hardwood cutttings, which usually leaves one or more dormant buds a short distance underground. In my own experience, and in warm climates and good soil, I would guesstimate the rates of re-sprouting as follows: about 60% for young vines (< 3 years old), and about 10% for older vines (> 10 years old). To increase your chances, Jugrnot, I would mix up several gallons of the following recipe, and drench the main root area with it:

4 tablespoons of organic sugar
2 tablespoons of fish emulsion
1/2 teaspoon of Epsom salts
1 gallon of water

If you can get hold of them, adding a teaspoon or so of humic acid and/or yucca extract will help it to absorb into the roots.