Is there always a need for a salt bridge to let a galvanic cell work continuously?
It depends where and how the electrodes are positioned. The UC Davis ChemWiki page Electrochemistry 2: Galvanic cells and electrodes describes the possible arrangements.

For example, if the electrodes are placed in the same vessel, a salt bridge is not required (as shown below). Ions can pass through the porous barrier.



If, however, the electrodes are are placed in separate vessels (such as in the diagram below), then a salt bridge is required to facilitate ion movement.