Could a golf ball damage an airliner?
Turbofans on commercial airliners are tested against hail, up to 'golf ball size', and ice is harder than a golf ball. 

Think back to Taca 110, that lost both engines while descending through a hailstorm reported to be up to golf ball size. What killed the engines wasn't the impact of the hail, but the amount of water ingested into the engines. It seems that the engines had been tested for water and hail ingestion at cruising speed... not at near idle, which was the power setting during a descent. Once identified, that problem was rectified quickly with mods to the engines. 

Nor does the golf ball have the sheer mass of a goose, such as the flock of geese that took out both engines of USAir 1549. 

Most likely, a golf ball striking a running turbofan would be sliced up by the front fan, and centrifugal force would tend to fling the fragments outward where they would exit via the bypass, and not through the turbine engine.

So I'd have to say, very unlikely, only to allow for the chance in a billion that the sliced up fragments of a golf ball might actually enter the compressor stage and cause a problem in one engine. 

The greatest problem from a golf ball being ingested by a turbine, is figuring out what rule of golf applies... how do you mark your card? (WTF probably doesn't meet approved guidelines)