It does even out, but it takes time. Right now, your muscles are working overtime to avoid the pain that the OA gives you, and your body is working differently than it should. The muscles are tight and getting tighter from the stress.
You are also structurally different in that the cartilage that your body needs to be there is diminished or gone. Mostly though, in my opinion (not a medical person here), the pain itself causes you to compensate and any extra effort (like balancing) is made problematic.
After the surgery, the structural component is restored. Not as well as the original, but close enough that we can work with it. After one year, I can balance on the left hip (my first) well. The right is still a work in progress, but I am looking for specific goals - martial arts kicks and their balance requirements.
There are many exercises that a good PT will give you that will help greatly with this. So yes, in my experience, my balance, strength and overall fitness of the hip is much better and already close to what I had before.
I definitely had the same thing. My muscles were incredibly stiff, my range of motion was horrible. I still kept playing all of my sports as long as I could, but they fell by the wayside one at a time. The last was soccer, but even that I left because of the tightness, lack of balance and pain. I think you'll be fine, but it is a long road and demanding.
After the surgery the results are immediate, though - no OA pain, and every step forward takes you out of the OA hole. A year's time and you'll be so much better, you'll be amazed (in my opinion, based on my experience).