Does numbness after hand surgery go away?

Depends. It depends on how severe the numbness was before surgery and for how long you had your symptoms. If your surgery was to repair a cut nerve, it can sometimes take 12-18 months for sensation to return and it may not be 100%. If surgery was done because your nerve is under pressure (as in carpal tunnel syndrome), the numbness may resolve quickly if your symptoms were not too constant or chronic.
It should unless... The surgery is to repair a nerve. Even in this case the numbness should eventually improve as the nerve re-grows (takes about a month for the nerve regrowth process to "rev up" and then the nerve regrows at the rate of 1 inch/month. Any other surgery should not be associated with long term numbness, but temporary numbness can occur with many different hand surgery procedures.
For most. It all is based upon where you start from and how healthy you are and timing. I like to use the water hose analogy. If you run your car over your garden hose for an hour the hose stops and the plants dont get watered. For a few days they may wither but they and the hose will do ok after. If your car is parked on the hose for months, the hose doesnt work well after and the p;lants may not recover.