3D? no, I have some modeling experience, but no real 3D animation experience outside of a simple turn-about.
2D? yes and no. I CAN do animation that is decent like that, but it would take the entirety of the jam to make a single 5 second clip. I can work on this for 2-3 hours a day, and that means I would take a week to do just the lines of a dragon lair style animation (even if I do only 6 frames per second (extremely choppy), that would still be 30 full drawing for that 6 second clip. Add the time to clean, color, import, etc, it is not feasible. Cluefinders (an edutainment game series) is way more feasible. They had static backgrounds and simple 2d animation overlaid that would be reused for each scene.
Also, we only have a month. You won't have time to learn enough programming in that time. (also, the game you posted about in your post is not strictly 'edutainment'. It sounds like an action/turn based games set IN the past, but not with the intent of TEACHING about the past)