I have an aluminum pot and just drop my wort chiller in the last 15 minutes of my boil and I have had no issues. Mine doesnt hang over the edge so I dont have to worry about taping it, so I can't help you there.
However, I do store my wort chiller in the pot when I am not brewing, so if there is any reaction from contact time, I have not seen it. My wort chiller has been sitting in my brewpot the past 6 months, minus the time im cleaning the pot and the beginning of the boil.
So RDWHAHB and just toss it in