No. Size is the dominant factor. Lifespan and what stages of fusion it undergoes are dependent on its size. The more massive the star, the shorter its life span. Red dwarf stars can live for trillions of years, but massive stars may live less than a billion years.
Notice that haiguise wrote "at the core temperature of the Sun." A more massive star has a higher core temperature, and thus haiguise's sentence about fusion rates would no longer apply. Fusion rates are faster at higher temperatures, and that's why more massive stars burn out faster. Notice haiguise wrote "T^4" and "T^20." Our sun is roughly 5000K. Massive stars can exceed 10000K. At twice the temperature, T^4 and T^20 imply 16x and 1,048,576x fusion rates, respectively.
But what is the effect on lifetime of not having any CNO present? If a present-day massive star would have a lifetime of 10 million years, how long would it live if it was a population III star with no CNO?
Carbon is formed in small amounts by normal stellar fusion, and since it is a catalytic process the carbon is conserved. So even an early star would probably have some fusion happening via the CNO cycle.
I'm not sure. I think a lack of metals makes a star less stable and burn out more quickly, but I could be wrong on that. There's some episodes of Astronomy Cast and Ask a Spaceman that I think would answer your question about pop3 stars more reliably than I could.
Would that mean that massive first generation stars could live longer than their current brethren, since there wasn't any C, N, or O yet?