Short answer: NO. Long answer: also NO.
Here's why: Rabbi Yosef Karo writes (Shulchan Aruch, Orach Chaim 328:2):
מִי שֶׁיֵּשׁ לוֹ חֹלִי שֶׁל סַכָּנָה, מִצְוָה לְחַלֵּל עָלָיו אֶת
הַשַּׁבָּת; וְהַזָּרִיז, הֲרֵי זֶה מְשֻׁבָּח; וְהַשּׁוֹאֵל, הֲרֵי זֶה
שׁוֹפֵךְ דָּמִים
Someone who has a life-threatening illness is commanded (מצוה) to
violate the Shabbos to preserve his life; someone who hurries to do
this is praised; someone (who pauses and) asks about this is a
murderer.
Mishna Berura there (328:6) follows up:
....ואם החולה בעצמו מתירא שיעברו עליו את השבת, כופין אותו ומדברים על
לבו שהוא חסידות של שטות.
....if the patient is afraid to have Shabbos violated for him, we
force him to violate Shabbos, and try to convince him (lit. "speak to
his heart") that this [not violating Shabbos in a dangerous situation]
is idiotic.
See also Shemiras Shabbos K'Hilchasa (by Rabbi YY Neuwirth) 32:5 (in my third edition [Feldheim, 2010 (blue cover)], volume 1 [Most of the time when I cite Shemiras Shabbos K'Hilchasa, it's from the second edition (red cover); I misplaced it today, and borrowed someone else's for the purposes of this answer]) says that if someone were to decide that he would rather not have Shabbos be violated on his behalf, we try to convince him to save his life, telling him that he has to; if he doesn't listen, "אף כופין אותו," we'll even force him to save his life through Shabbos violation. (MB 328:6)
חולה שיש בו סכנה....שמסרב לחלל את השבת להצלת חייו....אף כופין אותו
A patient who is in danger of his life....who refuses to violate
Shabbos in order to save his life....we even force him (to violate
Shabbos to save his life).
In a footnote there (16), Rav Neuwirth cites Pri Megadim (328:6) who writes that this is the case even in a case of possible danger to life.
I would also violate Shabbos to save the life of someone who is committing suicide -- see Hilchos Rof'im uRefuah (rulings of Rabbi EY Waldenburg on medical halacha, compiled by Rabbi Dr. Avraham Steinberg; Mossad Harav Kook, 1978), 2:2:11:
מי שמאבד נפשו לדעת....מותר לחלל עבורם את השבת.
Someone who willingly endangers his life....we may violate Shabbos for
him.
He cites Magen Avrohom to Shulchan Aruch, Orach Chaim 329 (number 5), as well as many תשובות (responsa) from many and varied rabbis in support of this argument.
For more about suicide on Shabbos, see Violating Shabbos for a suicide emergency.
Human life is more sacred than Shabbos -- Shabbos must be violated to preserve life, in any instance. One is not allowed to opt out of this מצוה.
