I went through withdrawal from Effexor while still in the first trimester. It was awful for about 3 months, but my baby didn't seem to have any problems. She's now a healthy one-year-old, despite my Effexor use (was on it until 7 weeks), and a different drug that I was put on at 7 months. I even breastfed, and never noticed any problems with her. She didn't appear to go through withdrawal when I weaned her either. In fact, the only thing I noticed that affected her was that she was a little cranky when I finally came off the Advil/Tylenol combo I was on for my stitches.
Because antidepressants like Effexor stay in your system for a couple of months, there is always a chance that it could affect the baby. My experience was great, although I crashed really hard once it was completely out of my system.
Get a doctor you can completely trust, and talk about all of your questions. If you don't get answers, try another doctor. And I wouldn't have ever dropped Effexor cold-turkey if I hadn't gotten pregnant...you might want to have a doctor monitering you closely through the next few weeks...withdrawal is painful.
Good luck!