You are correct. Another expression that's used is "on the dot." 7 o'clock sharp and 7 o'clock on the dot mean the same thing.

Shayne already answered perfectly, I just would like to add: Sharp, in other contexts may mean that has an edge very prone to cutting, such as a knife or an axe Eg.: This axe is very sharp And it can be used as a way of saying "clever". eg.: Mark is quite sharp on his answers