The city will grow every day, even if it's only a few per day, and the rate will increase as the pop increases. It won't take six months to hit max pop. And even then, you don't have to hit max pop before the city is capable of sustaining a decent economy.
But yes, it will be a few months before it's back in top shape. That's what happens when an entire city gets slaughtered to the last man, woman, and child.
