All women are different. I didn't leak until after I started nursing. But I know women that had to wear breast pads during pregnancy. It's hard to say.
I'm not sure what the "normal" time frame is every woman is different. And there it is hard to tell what is "normal" when it comes to pregnancy. I am 27 weeks pregnant and i have been leaking here and there for two weeks.
To be honest, I am almost 8 months pregnant and I noticed that I began leaking as early as 5 months. Your milk won't come in until a few days after you have the baby, but your body begins producing colostrum at about 4 months. Some women can leak colostrum, or pre-milk, as early as that time, or some may not begin to leak until after they have the baby.