Is it wrong?

Is it wrong or against the rules for me to drop my live chess rating from 1200 to 600?

Why would I do such a thing? I am curious about how opening play, frequency of mistakes, positional play etc change as a function of level.

I figure in the end I would end up close to 1200 again.

Deliberately dropping your rating to play against weaker opponents is known as sandbagging.  Sometimes used to get into easier tournaments to have a better chance of winning.

If you are very clear to your opponents (both on your way down and on your way back up) about what you are doing, and you stay out of tournaments/team matches/any other games that have any particular importance while your rating is lower than your true strength, it might be OK.

Yeah, it's against the rules. What MGleason said and also I think it's annoying to players when the ratings are totally off. One of the main functions is to pair players of somewhat equal skill. So on your way down you're wasting their time (either by resigning early or making obvious big blunders) and on your way up you're wasting their time (much better than them).

If you keep the games at least a little interesting for your opponents and don't advertise your sandbagging, you probably wont be caught and I'd think no harm no foul.

Moral questions aside, a 1200 playing at a 600 level is going to play differently from an actual 600, so you're still going to throw off your results. If you're looking for unbiased examples, you'd probably be better off searching through the finished games of other players.