Yes. Most shaft speed sensors are reluctance sensors that trigger when a piece of ferrous metal passes by them. The sensor will register each time the tab of metal on the shaft passes by.
If you manually do it I think it would be hard to register on the speedo but if you used something to spin a metallic item by it, say chucked in an electric drill, you may be able to get it to register.
A reluctance sensor does not require a magnet to pass by as a Hall Effect sensor does. It's not practical to magnetize parts of the transmission so they use a reluctance sensor instead.
You could also simulate the signal from the sensor with some kind of a circuit drive by a signal generator but you would need to determine the characteristics of the signal and duplicate that.