The experience of many countries—France being the most commonly cited—shows that's not a problem. Quite the contrary, voters turn out at the same rate, if not higher, for the second round because the choices are so clear at that point. For that reason, it's the system I prefer.
On the issue of representativeness, what matters is not the representativeness of the opinions expressed but, rather, the representativeness of the person chosen as the member.