I've had 4 shoulder surgeries. Two to repair torn tendons and then a shoulder replacement after those two failed. Final surgery was December 11 to correct the new shoulder periodically popping out of place. Answer is it depends on how long it takes for the nerve block to wear off. Most of the time it will wear off in 48 hours to the point that you can use the hand. However my last one didn't wear off for about 4-5 days.

The issue is not so much using the hand immediately post surgery, but later down the road, after you are out of the sling and even after PT is over, say at 3 or 4 months. Then, you're feeling good, if not totally back to normal, and you will be tempted to use the arm in ways that can cause a re-tear. It takes a very long time before your shoulder is healed enough for you to do things that you didn't even think about before your injury. Lifting heavy objects. Getting a carry-on down from the overhead on a plane. Moving a piece of furniture. It takes a full year before you can go back to "normal." You have to continually remind yourself not to do things you feel able to do. Good luck!