Yes, Auto MDI-X (invented and promoted to IEEE in 1998 by HP) is an optional part of the 802.3AB 1000BASE-T specification, that has been widely implemented. So, you may run into a 1000BASE-T NIC without it, but I doubt it highly in this day and age.
Keep in mind 1000BASE-T is not the only type of Gb networking, just the most common.