I strongly believe that it makes a big difference to be in great overall condition, but also specifically around the hip area.
Here is my own experience: With my first hip 10 years ago, I was on crutches due to a failed stem cell injection for over six weeks prior to surgery. Though I am usually in very good shape, I entered that surgery way below my norm, especially since that leg had very little weight bearing for six weeks prior to surgery. With my second hip 8 months ago, I was in very good condition, and skied hard eight hours a day, every day, right up to the week before surgery, even though I could barely walk after skiing. I think that high level skiing is one of the best exercises there is for strengthening and toning all of the hip muscles, since there is a lot of powerful lateral moves, as well as a lot of internal and external rotating moves. The difference in the recovery was dramatic, with the second recovery going much faster and easier than the first, even though I was 67 the second time. By the way, both surgeries were with Dr Gross, so you are in excellent hands.