Can the serial input of a parallel input/serial output shift register be used as an additional input?
Yes, for reading switches, you could do that. After a parallel load operation, the first 8 bits would come from the switches connected to the parallel inputs, and then all of the bits after that would come from the ninth switch.

Of course, you could connect another shift register to that input and read an additional 8 switches, for a total of 16 or 17 switches.