It really depends on how the existing footings were installed. If the deck was permitted and inspected by the local building department, we can assume that they were installed correctly. If the footings appear settled, cracked, tilted or heaved they should not be reused. The next consideration is the deck load each footing is supporting. If the size of the footings is known, then the new deck design must not overload any existing footing.
The addition of a roof or shading structure over the deck must also be considered. These features apply additional loads on the foundation and must be evaluated. In most cases, it should not be assumed that the existing footings could support additional loads from these features.