18mm baltic can be quite stiff. If the bow can be straightened and held straight it may be OK, like if you put the bow in the middle, touching the bottom, and pull the front and back in. It may depend on how wide the side boards are.
If the 1/2" maple ply is cabinet grade (which is appears to be) and not Chinese. and if it has actual wood in it, it probably will stay flatter than baltic birch. The core laminations tend to be fir or poplar which are both nicely stable. BB plywood tends to be mostly flat, but it is rarely completely flat. Birch is an unstable wood and laminating it only makes it kind of more stable. BB's main advantages are screw holding ability as noted above, no voids, and (formerly) cost. And it looks reasonably good, including the edges.
If you are careful, screwing into the maple ply for drawer slides will work just fine. Honestly the corner joints can be glued and screwed/nailed butt joints (pilot and countersink the screws). The face veneer on cabinet plywood is very thin and prone to tear out, which is more of a negative for a kitchen or furniture piece than a shop drawer. But given the option, orient the long side with the face grain to minimize tear out, or put the "cross cut" pieces on the back.
Prior to introduction/common use of BB plywood in the 90s, kitchen drawers were generally made of cabinet grade fir or even solid white or sugar pine, all of which are softer than birch. Hardwoods were also used, but those tended to be more premium, not your average kitchen.
Unsolicited advice
Always buy at least one more sheet of baltic birch than you think you need, unless it is readily available at the store. It is handy enough for jigs, fixtures, kids furniture, etc, that it is convenient to have some on hand. Plus you'll be covered for unforeseen instances, like when I reversed the dimensions on some drawer sides with the front&backs on my last cabinet build.