Is it possible to create a double layer PCB by gluing together two single layer PCBs?
In my opinion it is always possible to have a single layer PCB with trough hole componentens, if the size does not matter. Sometimes you need a lot of wirebridges, but you can do that pretty neat, as in the pcb I made some years ago:



If you really want to go for a double sided PCB, what you say seems possible to me. If you drill some pads that are both on the top and bottom PCB before sticking them together, you might even be able to fix the two pcb's just by soldering the wires on the top and bottom pads. Onther option is to drill the mounting holes on both pcbs and use some nuts and bolts to hold them together while you solder. Afterwards you can drill all the holes for the component leads, so to match exactly.

If available you might want to use 0.8 or 1.0mm material instead of the standard 1.6mm so to prevent problems with e.g. DIP IC's that have pretty short legs.