Does it matter? If someone may or may not be an actor by your judgment is going to cause you to possibly commit an atrocity then you should play it safe and refuse. Just in case...

It matters for the validity of the experiment, yes. Bear in mind, the chances of the experiment being real were astronomically small, as university professors are not normally in the business of torturing members of the public. As there were (iirc) small rewards given for taking part, the rational thing to do is follow the instructions. This seems like an inherent problem for attempting to study order-following in a lab.

And of course if you were a participant in the original experiment, you'd tell people, "Of course, I knew it was just an experiment, and it wasn't really happening."

You'd start by telling yourself that, so it would be easy enough to convince people looking to "debunk" the experiment later.

They told Milgram himself and he hid the interviews. From the second link above,

The new research builds upon findings from a previous study, which analyzed recordings of 91 conversations conducted immediately after the termination of the experiments. The recordings showed that most of the obedient subjects justified continuing the experiment because they believed the learner was not really being harmed.