Can both the overlapping genes (in opposite strands) produce proteins?
While overlapping antisense RNAs are quite well known, there are very few examples in which both the RNAs from the pair can code for proteins. However, it is not impossible. I can cite one validated example: RU2S (DCDC2) and RU2AS (KAAG1) pair.

While RU2S is constitutively and ubiquitously expressed, RU2AS is specifically expressed in kidney, bladder, liver, and testis. It is also expressed in certain tumours (Peltz and Dougherty, 1999).




 Peltz SW, Dougherty JP. Antisense Translates into Sense. The Journal of Experimental Medicine. 1999;190(12):1729-1732.