That would unquestionably activate their belief that this person is still alive and they would consider such an action to be murder. You could play their two beliefs "this person is alive -> don't murder them" and "at least as a soul instead of a vegetative patient this person would have some autonomy" off against each other but they would most likely back out of the conversation before any serious mind-changing happens.
For your consideration, a psychology study as summarized by The Economist in "How dead is dead? Sometimes, those who have died seem more alive than those who have not":
The study is "More dead than dead: Perceptions of persons in the persistent vegetative state":
Ed Yong points to another interesting study, the 2004 "The natural emergence of reasoning about the afterlife as a developmental regularity":
Jach on Hacker News makes the obvious connection with cryonics; see also lukeprog's "Remind Physicalists They're Physicalists".