Yes, the wheel speed sensors can detect if the vehicle (or at least the specific wheel the sensor is tied to) is moving. On most vehicles you should be able to tie directly into the wheel speed sensor and detect the signal, while not causing any issues with the vehicle itself while in normal operation.
The sensor itself is a standard sine wave orientation. It's either on or off and is predictable. If there is movement in the signal, there is movement in the wheel sensor and movement of the wheel which is attached to it. Depending on how old the vehicle is, it could be a two or three wire speed sensor. I believe both of them work basically the same, but the three wire sensor is going to be more accurate. It uses what is called the Hall Effect, where you have vehicle voltage as the base reading (using two of the wires), then the third wire picks up the signal. On the other side of the equation is the stator which has equidistance notches in it which pass by the sensor and causes the signal. In order to use it, you just need to figure out which is the signal wire and then tie into it to get the signal. If you have a device which can detect the Hz which is produced, you can calibrate against the speedometer or GPS device to figure out how fast the vehicle is moving.