I guess I could.
Well, as I twisted it in, it felt and sounded to click into place. It wouldn't screw in any further and it wouldn't back out either. Turns out to mount it on completely, or remove it, I would have to hold down the K-mount's release button. That was because the little protruding piece connected to the release button seems to stick itself into a dark little crevice, home to one of the three screws on the mount's surface.
This left me so dumbfounded, since before mounting the adaptall, I scanned it's mount to make sure it wouldn't "lock" itself onto the m42 adapter. This goes to show that I should be checking all of the gear involved beforehand, instead of just the new one.