If it is in writing, and properly executed, there is no reason to doubt it would be upheld.
Then the only challenge would be to show the document is a fake or had been surperceeded by another document (like a new will over an old will)
Since Terri has a constitutional right to life what difference is there if she signed this or a cocktail napkin? Suicide pacts are OK if the party becomes unconscious? This paper, or Terri's verbal wishes, allows, even provokes her guardian and health care provider to be murderers?