I went away for about five days and left a roll of Canon Satin Photographic paper (7 mil, 190 gsm) loaded in the printer. I turned off the printer before I left. The first print I made after I came back showed four dents made by the rollers attached to the auto roll feeder unit, exactly 1 1/2 inches from the leading edge.
I've also noticed some very shallow dents in the Canon Fine Art Bright White (20 mil, 330 gsm) after just a day or so of non-use. The light has to be at a very steep angle to see them, though. The printer was on, but sleeping, during this time.
So, I recommend that you not leave roll paper loaded for very long, or at least plan on trimming off the first 1.5 inches (3.8 cm) if it's been a few days since you used the printer.