From the Gatherer rulings:
If your life total is negative, X is considered to be 0. (This is a change from previous rulings.)
The actual comprehensive rule that supports this is:
107.1b Most of the time, the Magic game uses only positive numbers and zero. You can’t choose a negative number, deal negative damage, gain negative life, and so on. However, it’s possible for a game value, such as a creature’s power, to be less than zero. If a calculation or comparison needs to use a negative value, it does so. If a calculation that would determine the result of an effect yields a negative number, zero is used instead, unless that effect sets a player’s life total to a specific value, doubles a player’s life total, or sets a creature’s power or toughness to a specific value.
So in other words, you can actually have negative life, and your life is treated as being negative, but not for the purposes of calculating an effect such as Death's Shadow.
Shortly put: No, but it used to.
GendoIkari already gave the current and correct answer, which is No, however it was not always the case and this change was relatively recent. 107.1b used to have one additional clause for when negative values were used in calculations which was:
"...unless that effect sets a player’s life total to a specific value, doubles a player’s life total, or sets a creature’s power or toughness to a specific value, or otherwise modifies a creature's power or toughness."
This was revised with the release of HOU to the current version we have now.