Depends on what material the doors are made of.

Some fasteners might still be a good idea.

Get a doweling jig, and use dowels and wood glue. Also make sure you clam the doors straight and flat while the glue dries.

Putting a couple of pockethole screws in from the top and bottom would also help

Can that be done? Yes.

Should it be done? I doubt it.

The reality of modern adhesives is the glued joint is often stronger than the rest of the material. Use modern wood glue does that. A joint is glued properly and that joint will not break---but the wood near the joint will break if the stress point it reached.

Glue the joint improperly and it will fail quickly.

A properly glued joint has to be clamped and the two edges have to be exactly level to each other.

Edge gluing two doors together would require 20 or clamps(pipe clamps probably) and cauls(mechanisms to level the door surfaces) to keep the two doors on plane.

If you need to buy those clamps, figure on $12 to $16 a set of clamp fixtures and 20 pieces of pipe(threaded on one end) that are at least 8' long(10' might be better).

Prepping the two edges will take a very skilled hand tool craftsman or a rather expensive power tool.

All together, it will probably be better(and maybe less expensive to have a door made to order.