A:Answer According to the website Battery Junction, no they are not equivalent.
For CR-123, these are the listed "associated" battery sizes: 123, 123A, 2/3A, 5018LC, BR2/3A, CR123, CR123A, CR17335, CR17345, CR23, DL123A, EL123A, K123LA, L123A, SF123A, VL123A
For A23, these are listed as "equivalent": 23, MN21, R23A, 21A, GP23, 23A, 23GA, A23, E23A, GP-23A, GP23A, K23A, l1028, LR23A, LRV08, LRVO8, A23BP, A23BP-2, MS21, V23, V23GA, VR22 Batteries