Usually they have a worn gear drive so, "No" it most likely wouldn't turn. Often times the grease in the gear box can harden to the point that the motor won't turn, or if left on long enough burn up the motor. Electrical contacts can get corroded too. Did you check the fuse?
1. Check the fuse.
2A. Put a volt meter on the connector. You can just run it to chassis ground on the - side. Turn on the wiper at each position and then look for voltage on each connection point. You should only find voltage at one point per switch position (other than off*). The one where you find no voltage after going through each position is likely ground. *You may find one wire that has voltage all the time as something like that is needed to get the wipers back to the "park" position.
2B. You can set a voltmeter to Ohms and check for continuity on the motor. Unfortunately I have no idea what to expect to read at any given connector. So, it can be a bit of guessing what thereadings mean. Maybe others are more versed on that.
3. Assuming you have voltage at the connector you might want to open the gearbox case and look at the condition of the grease. There are often wipe tracks of copper on a circular board and any corrosion, hardened grease etc. can disrupt electrical contact.
So, that should get you started.