I am sure it is possible. I know that mine is gone sometime in the first trimester. I don't remember when. This is one part of pg that I don't like...
Jackie and Rafael (4/15/04)
DS (4/25/05) my unschooled airbending pokemon wizard
DD (10/05/06) my spirited pixie, who weaned at 3 yrs 10 months
DD (7/27/09) my UC water baby - I mean toddler!
DS (2/21/12) UC #2! My littlest love
I lost my milk before I even got my BFP. DD started complaining about it right away. I did everything I could to keep my supply up, but it was completely gone before 2nd trimester. We continued to nurse through pregnancy and are still tandem nursing (almost 10 months in!)
SAHM to Chloe«- 6/2008 (10 lbs, 5 oz), Hannah- 9/2010 (9 lbs, 12 oz), Liam- 2/2013 (9 lbs, 6 oz)
Before I even got my BFP my son was trying to nurse all night. He calmed for a week or two but started in again. My bb's feel empty all the time now so I'm pretty sure there isn't much left. I'm still nursing him on demand for now but if it gets excessive (more than 3 at night and 3 in the day) I distract him and avoid it. He is 19mo but doesn't take other milk.