It is possible to do this with Ghostscript and the pdfwrite device, but its by no means simple. You need to write some PostScript to do the job.
You would need to add BeginPage and EndPage procedures, the BeginPage would need to check the current page number (and you would need to track this yourself). If its page 1, process normally. If its an even page, throw away the current PageSize and replace it with one which covers a pair of pages. Process the even page. Do not transmit the content.
If the page is odd (and not 1) then translate the origin so that its offset to the right by the width of the page. Process the odd page. use moveto, lineto and stroke to draw the required line between the two pages. Transmit the page.
This assumes that all the pages are the same size and orientation, or least that the sizes of each page are known in advance. It would be possible to retrieve those programmatically as well, but more complex.
Its definitely non-trivial, but if you rummage through my answers in the PostScript tags and look for anything with the word 'imposition' you'll probably find program outlines to do the job.
I did a quick look and here's an answer I wrote some time back. It uses a different approach to that outlined above, it copies some of the guts of the PDF interpreter and repurposes them. It does a chunk of what you want though.