I voted "yes."
I have been in my girl's lives since they were 3 1/2 and 18 months, respectively. In the beginning, while we were dating, I deferred to my DH for most disciplinary actions, while the kids and I were adjusting to one another. After my DH and I were together for about 9 months, our oldest came to me and very tentatively said, "You're more than just Sarah. Can I call you mama?" I of course said yes, after consulting with my DH and the ex. Bio-mom has never had a problem with the girls calling me Mom, Mommy, or Mama. Now, I discipline the girls in the same way I will their future siblings. No, you can't paint your bedroom walls. The banister is not for climbing. I've asked you three times not to throw things at your sister...why don't you go calm down in your room for a little while?
I agree that you have to figure out what works best for you as a family. Of course on the big issues (like the day our 6 year old told me that it didn't matter how she was punished, since she doesn't have to stay in our house that long anyway) I talk to my husband, and he usually handles it. I fully accept my role as a parent, and never correct someone when they ask how old "my" kids are. If the girls don't object, why should I? However, I understand that there are going to be some "growing pains" issues, especially with the way the ex raises the girls (no discipline, to the point of watching TV at 3am if they don't want to sleep) that will require my DH to take a more "leading" role. He's always very clear though that Daddy *and* Mommy said XYZ.
We're all in this together. As long as the ex doesn't have a problem with my being active in the kids' lives, why should I? They spend time in my home, eat my food, I do their laundry, quiet their nightmares, and they call me Mom. I'm honored and blessed.