This is a very good question, and one you'll need to ask your surgeon. There are many factors here. The position you're in for the operation is certainly an important one. In some cases the patient is on his or her back with the legs apart (flexed and separated). The surgeon actually stands between the patient's legs looking toward the patient's face.
Your hip range of motion will be greater under the influence of the anesthesia than it is when you are moving it yourself. But there's a danger of hip dislocation if the hip isn't supported or if the hip is moved too far out.
The surgeon will test your hip motion and check the joint for stability before doing any surgery with extreme positions. Still, it's always a good idea to remind the doctor of any special considerations.