Does that mean that someone like Voldemort, who was obsessed with immortality and therefore unwilling to accept death, can never master the Elder Wand?
It depends on whether you're saying that the words 'facing' and 'accept' mean the same thing.
Facing (at least the way I believe you are using the word) means to:
confront and deal with or accept a difficult or unpleasant task, fact,
or situation. "honesty forced her to face facts"
Accept (at least the way I believe you are using the word) means to:
consent to receive (a thing offered). "he accepted a pen as a present"
While they are similar, they do not necessarily mean the same thing. You can face something, and not accept it (e.g. your mother telling you that she has your best interests at heart while she force feeds you broccoli, at the same time that you're trying to close your mouth as tightly as you can). The way you're asking the question, you are implying that to face something and to accept something are the same thing. However, they are not.
So, to answer your question...
Voldemort could theoretically face death and become the true master of the Elder Wand without having to accept it (which is what he is actually not willing to do). I would argue that at any point in the series, if he had the Elder Wand (and had successfully taken it off the previous owner himself) he would be able to use it, because he is facing death the entire time he is trying to become immortal. The difference is that he hasn't accepted it.