In reply to kevin stephens:
Obviously going to be up to the wall in question. Main issue with climbing in normal outdoor shoes is contaminating holds with whatever you so happen have stepped in all day, this then gets on folks hands, in cuts/grazes, in mouths and etc. If I was floor walking, and the place wasn't too busy, I'd probably think it was quite amusing and let you away with a couple routes. Could be issues with you damaging holds, wouldn't want you connecting with anybody on way down on autobelay, and wouldn't want it to become "a thing". Sure someone will be along soon to point out it would be incredibly irresponsible and dangerous, followed closely by someone pointing out that that's what climbing's meant to be.