No they don't. But I like that at least the folded wings give the arms a "stopping point" in tank mode.
After owning him for a while, the side to side hip swivel and knee joints have started loosening (which were already pretty loose when I bought him). This a bit of a design oversight: they are simple pinned through, not ratcheted. In robot mode he's quite top heavy so if leave him displayed in a wide stance dynamic pose, gravity will weaken the joints. Worse still, 5 of the 6 modes require engaging and disengaging the double knee joint, which puts a lot of force on the regular robot knee joint. I gave the joints a coat of clear nail polish, which made him hold poses better, but the knees are still quite weak because it's quite tricky to get the nail polish in the seams of the joint.