Oh yes, you will continue to produce milk for some time after your baby is born, until you stop breastfeeding in fact.
How far along do you have to be to develop milk
Your actual milk doesn't come in until a few days after your baby is born, what you are leaking is colostrum. You will know when your milk comes in and it is impossible to tell if you will produce enough before your baby is born. Women seldom have production problems you just have to dedicate yourself to not quitting and nurse your baby all the time. Good luck!
I have this happen too, and it ends up leaking all night. :( I'm 32 weeks :)
Its all normal, i have been producing milk since i was 10 weeks pregnant and iam not 30 weeks.
I haven't breastfed in 3 months and still leak milk. I would love to keep breastfeeding but my son has gotten greedy lol and won't take it. He wants a bottle and veggies lol