Yes, but even that isn’t simple, I think. They’d not want to land on top of it, so they’d have to push it out from the lander or have it propel itself away from the lander. If they push it out and it doesn’t have a way to stabilize itself, keeping the lens pointing upwards then will require tight control over that push.

So, I guessed (see below) you’d need power to make the sat orient itself.

However, I googled a bit more, and found this: https://mynews13.com/fl/orlando/space/2024/02/21/embry-riddl..., which says:

“EagleCam will be spring ejected from the Nova-C class lander Odysseus about 30 meters above the lunar surface during the final descent. It will take three images a second from each of its three cameras (a total of nine images a second), capturing its six-second freefall to the surface and Odysseus’ descent and soft landing. About an hour after landing, our team will receive the five images of our choosing. During descent, Dr. Henderson and I will be timing events in landing sequence to match to image numbers to choose the first five images we bring back to Earth. Once we have those images, I will post them directly to @eraueaglecam on Instagram. Shortly after that, they will also be available on @spacetechnologieslab on Instagram and @SpaceTechLab on X (formerly Twitter).”

So, it isn’t a 360 camera, and they’re making 50-ish images and hoping for the best. Doesn’t look like the sat has rockets or that they’re trying to make it possible to make more photos after impact on the moon.

If my guesses/intuition is right we won’t see the actual touchdown (still cool to have anything, of course), but corrections welcome.