Life on Mars would have no impact on the strength of the cosmological ID argument. However, the absence of such life would land in the win column for privileged-planet type arguments. At the same time a lack of Martian life would be an easier pill for evolutionary biology to swallow.
If primitive life is discovered on Mars, some will say "see, not only is earth not privileged, not only is life not rare, but in fact it is so common that we find it on our next-door neighbor. Any discussion of one in a gazillion chance is clearly nonsense."
Bzzt. Sorry, the more sensible response is: the conditions for complex are exceedingly rare in the universe. And given that earth had to be in the right part of the right kind of solar system, with the right kind of satellite, and the right kind of star, and the right planetary companions, in the right part of the right type of galaxy, in the right cluster of galaxies, of the right age, in a universe with the correct laws and constants—well if I were taking bets on the next most likely place to find life, I'd look first at earth's nearest neighbors, reckoning that they are closest to being in the habitable zone. If I can't live at the oasis, I'll settle for being within walking distance.
If any place other than earth should have life, it should be Mars. If Mars has primitive life (that didn't originate on earth—that would have to be ruled out) then it is because of its proximity to a favored location in the universe—not a sign that life is cheap and easy.
Personally, I don't think we will find evidence of non-terrestrial primitive life on Mars. New data from the European OMEGA satellite confirms Mar's lack of substantial water, or of any significant hydro-activity on Mars for the last 3.5 billion years.1 So when there was water on Mars, the solar system was at its most inhospitable—with the inner planets subjected to frequent life-quenching impacts from comets and asteroids.
It's fun to test the predictability of evolutionary biology by asking those practiced in that science to predict what life on Mars will be like, should we discover it. If you get an answer (not likely) and distill it to its essence, it will be along the lines of "Oh, I don't know, but whatever it is will be consistent with evolution." Can you imagine a physicist stating "Oh, I don't know even the gross details of the orbit of Mars, but whatever it is it will be consistent with gravitation."
Then again, if I were an evolutionary biologist I would be hoping that no life was found on Mars. I would not want to explain how earth (without being privileged) supports complex life while microbes on Mars remained microbes. I'd much rather Mars be sterile, so that I could blame the great evolutionary scapegoat, abiogenesis. A lifeless Mars permits the argument that "yes the origin of life is (possibly) rare, but if life were to have started on Mars, it would have evolved (as all life should, evolutionarily speaking) into more and more complex forms."
To summarize, and perhaps counter-intuitively, non-terrestrial microbes on Mars would be neutral in its impact on cosmological ID. It would be problematic for evolutionary biology, which would have to explain why evolution was so impotent on Mars. A sterile Mars, or a Mars whose only life consists microbes emigrating from earth, would bolster the privileged planet arguments, and yet provide an escape for evolution, which could, as it always does, sweep its most difficult problem under the I'm-covering-my-ears-and-not-hearing-you-because-abiogenesis-is-a-different-discipline rug.
1 Jean-Pierre Bibring et al., "Global Mineralogical and Aqueous Mars History Derived from OMEGA/Mars Express Data," Science 312 (2006): 400-04.