This is, of course, possible. For a very special meaning of the word "possible": extremely expensive, dangerous (to the astronauts), and pointless.
This question reminded me of the Tu-4 - the Soviet reverse-engineered copy of the American-made Boeing B-29 Superfortress. Stalin had 3 B-29 which emergency-landed in the USSR during WW2, and he ordered Tupolev to copy them. This turned out to be a brilliant step: copying the plane (as opposed to creating a "better version suitable to the existing Soviet realities") required creating whole new industries and gave a huge boost the the Soviet aircraft technology.
Copying Apollo would have the opposite effect: resurrecting obsolete technology instead of creating the new ones.
Suppose we want to repeat Magellan's circumnavigation (yes, I know he died on the way). Would we build a modern ship to do that or re-create his caravels?