I put mine in the dryer when I first buy them and before hemming, because since all four of us do laundry, it is a distinct probability that sometime, someone is going to accidentally throw my jeans in the dryer. I would much rather get all the shrink out before hemming, because once you hem them, there's only so much material you can let out again later. Also by shrinking them right away, if they do shrink too much, I'm not "attached" to them so while it's sad, it's not devastating. I have even been able to return jeans that shrunk too much. But the place I get my premiums at, which does free hemming, stipulates you MUST run them through the dryer at least twice before they will hem them.
I do not think this has ruined the COH fabric at all. They do not bag any more or less, and I don't need to always throw them in the dryer. (Although if I am in a rush and need clean jeans faster than waiting around for them to air dry, I know I can safely throw them in the dyer). I worry more about the dryer fading them, than ruining the stretch.
My UO jeans - non-premium- I do put in the dryer rather frequently. The stretch has not been ruined, but they have faded.
As for the dryer ruining stretch, any stretch fabric will eventually deteriorate - even if you never wear it and just leave it in the drawer! I have had this happen with running gear. I tuck it away in storage, and the next year when I bring it out, the stretch is all gone.
Nobody can predict how much your Jbrands will shrink, or how they will shrink. Particularly hard to say how much will shrink on the length. I have had jeans shrink several inches. As for snugging them up (horizontally), my best guess is that they will snug up, but then stretch out again to right where they are at now.