Connecting Function Generator to Arduino
Sure, you can connect the function generator to an analog pin of the Arduino. The probe and the jumper wires are just wires here, nothing special. You should also connect the function generators ground to the Arduinos ground (!).

But: Be sure to stay in the Arduinos voltage range (0 to 5V) with the function generators signal. If you apply a higher or negative voltage, you can destroy the Arduino. As long, as you stay inside that range, nothing bad will happen.