You could well be right and that is an interesting approach.
I read the original question a little differently and assumed the poster (OP) actually wanted to turn the servo arms manually and capture the movements in such a way that the record could be used to program a micro. That might be possible, but it would involve hacking into each servo to capture the position information. I do't think it would be possible by trying to capture some sort of signal data from the servo lead.
Here is a link to what a hobbyist found in a typical, cheap servo. The main chip is made by
Agamen. The link I have to the datasheet for the
AA51880 is not working today, so I did a screen print to capture the important stuff to this reply:
Note the sense resistor (VR1) near the servo motor. That is one place where the OP might test to get information about the manually controlled positions. If one were to take that approach, I suspect it would have to be done power off. With power applied to the servo, manually moving the servo arms could damage the servos, depending on the type of servo being used. For any servo, current draw would be quite high, if held out of position.
So, I think bigdogguru has the best solution, even if that is not what the OP intended.
John
Edit: The four asterisks should be the word, "****." For some reason, the site relplaces my word with the asterisks. I hope it is not considered profane.
Edit#2 : H_ac_k is apparently not allowed. So I changed to "test."