Can I run a sink drain through the wall to connect back where it was before relocation?

I want to know if it is an option to run the drain along and within the wall where the new sink sits and back to where the old sink drain is.

Another option would be to connect to the drain of the sink (shown in the left side of the image) that is in the kitchen adjacent to the same wall where the new sink is installed.

The shower heads will be located in the corner.

Here is the current layout.

and here is the new layout.