If this concept is considered from the viewpoint of Sefer HaChinuch 296:1, it is found that this idea of living by them is associated with the mitzvah of sanctifying G-d's name, just as to die by them is.
מצות קדוש השם - שנצטוינו לקדש את השם. שנאמר (ויקרא כב לב) ונקדשתי בתוך בני ישראל. כלומר שנמסר נפשנו למות על קיום מצות הדת. וכבר בארו זכרונם לברכה מפי הקבלה ומן הכתובים באי זה ענין ובאיזו מצוה נצטוינו בזה, ואף על פי שכתוב בתורה וחי בהם, דמשמע ולא שימות בהם כבר קבלו הם, שלא נאמר מקרא זה בכל ענין ובכל עברה. ומפי הקבלה אנו חיין בכל דברי התורה.
That in either situation, whether to live or to die, the concept of mesirat nefesh מסירת נפש (to surrender, or deliver or hand over ones life) means to sanctify G-d's name לקדש שמו ב״ה in regard to fulfilling the commandments like is seen in regard to Yosef HaTzaddik in Sotah 10b.
א"ר שמעון חסידא יוסף שקדש ש"ש בסתר
Yosef did not die or sacrifice his life. He demonstrated his faithfulness meaning he sanctified G-d's name and continued to live.
In fact, this is also understood from Shmuel 1 25:29 which states:
וַיָּ֤קָם אָדָם֙ לִרְדָפְךָ֔ וּלְבַקֵּ֖שׁ אֶת־נַפְשֶׁ֑ךָ וְֽהָיְתָה֩ נֶ֨פֶשׁ אֲדֹנִ֜י צְרוּרָ֣ה ׀ בִּצְר֣וֹר הַחַיִּ֗ים אֵ֚ת יְהוָ֣ה אֱלֹהֶ֔יךָ וְאֵ֨ת נֶ֤פֶשׁ אֹיְבֶ֙יךָ֙ יְקַלְּעֶ֔נָּה בְּת֖וֹךְ כַּ֥ף הַקָּֽלַע׃
This phrase צרור בצרור החיים is commonly associated with when one dies. But as Sifrei Devarim 344:7 emphasizes this is actually emphasizing the acceptance of the Torah and it's commandments, commitment to fulfilling the commandments.
These are the souls of the righteous which are reposited with Him in the "treasure-trove," as it is written (I Samuel 25:29) "May my lord's soul be bound up in the bond of life, with the L-rd your G-d." "And they planted themselves at Your feet": Even though (at the giving of the Torah) they recoiled twelve mil and returned twelve mil," they bore (the yoke of) Your words — "All that the L-rd has spoken, we shall do and we shall hear."
לקדש, which means to sanctify or to manifest fidelity toward (fidelity means demonstrating faithfulness, loyalty and support) or to dedicate, as in להקדש ספר.
And so, וחי בהם means to dedicate ones life to the fulfillment of the commandments which is the mitzvah of Sanctification of G-d's name.
So even if limiting the question to Is וחי בהם one of the 613 mitzvot of the Torah, it would appear to be yes.