I did it twice last night and the stinger and pressure corks stayed put. The header cork popped out very slightly even though I ran a cork holding zip tie lengthwise around the entire pipe and I backed it up with a second tie around the pipe neck near the header opening holding the first tie very securely. The cork kind of bent itself around the wraps a little bit. The wraps did not move. There was very little escaped ice in this area and I doubt it had a significant affect on the process.
There was a slight improvement in my dent, but not much. I see a few flaws with this freezing process. First of all you cannot control where the ice is going to expand. The ice is not going to just pop out your dent. It could push out any part of your pipe including the good areas, thus deforming the pipe even more. You can try to stop this by running many tie wraps around the body (width) of the pipe to hold the current shape in the good areas. You would have to use a lot of wraps. The second problem has to do with dual chamber pipes. There is a baffle in these pipes and you cannot control what the ice is going to do to this baffle. It looks like the ice may have slightly enlarged one or more of the holes in my dual chamber baffle.