How can I make an OR gate out of two sockets
Is such design possible?


Yes, such a design is possible.

The problem is that it's not going to be easy to ensure safety. 


Your solution is going to require correct phasing of the plugs in both devices (L to L, N to N) or short-circuit will occur.
The big problem is that if one plug is in and on the other will be live.








simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. The live plug pins problem.

I advise you against combining the products in this way.