Oh, yes. It stretched, got uncomfortable, and popped-out during my first pregnancy. It was really, really uncomfortable, weird feeling, almost nauseating. And you're doing twins, so you're going to feel that moreso.
By my second pregnancy and beyond, it didn't bother me. It was almost "limp" when it it popped out the second time...like it was broken. Mine looks fairly normal now, after 4 big babies...although it's a bit lower than it used to be.
If it's really bothering you, you should talk to your doctor about it. It's possible to get an umbilical hernia dring pregnancy.