Is it possible / a good idea to use plywood for mortise and tenon joints?

Plywood doesn't really work with traditional joinery. Because it is made from alternating plies or other composite construction it is hard to make a snug tenon fit. Further, many of the joints will be mostly end-grain. Both of these issues make tight glue joints nearly impossible with those sorts of joint. And, though the outside ply will readily work well with PVA glues, the internal plies themselves may be constructed with glues and additives that do not work well with PVA. This generally makes for an ill-fitting, weak joint that does not take advantage of how PVA glues work.

You'll find most plywood construction is made with biscuits, dowels, or pocket screws. That is, most plywood construction makes use of fasteners for aligning and providing some additional stiffness.

Depending on the application, you might get away with finger-joints if that was a construction detail that appealed to you. It may not be tremendously strong, though. It may depend on the rest of the construction and the type of plywood. But it is generally a reasonable option for many.

Finally, I suppose you could experiment with what boat-builders do with plywood. They tend to use mechanical fasteners as well, but where they don't, they often use epoxies and other special adhesives with lap-style joints to provide strength with flexibility. A special case, maybe, but it points out one of the first major industrial uses of plywood materials.