Is protein folding symmetric with respect to reversing the sequence order?
No! Although there is a relationship, the protein would not fold properly since the C and N terminals are reversed consider the following: 

H(NH)-A-C(=O)(NH)-B-C(=O)(NH)-C-C(=O)(NH)-D-C(=O)(NH)-E-(C=O)OH

as appose to :

HO(C=O)-A-(NH)(C=O)-B-(NH)(C=O)-C-(NH)(C=O)-D-(NH)(C=O)-E-(NH)H

These are completely different molecules! 

http://www.ncbi.nlm.nih.gov/pubmed/1604320 http://www.pnas.org/content/95/13/7287.long http://www.pnas.org/content/111/32/11679