Maybe with Python.

Otherwise, no way that I know of. Creating a New Master and toggling animatable in settings will record some change in the dependency listing, though no change will act in the dialed dependency... So not possible to connect settings options to a dependency.

Certain properties such as Visible and Joint Editor settings such as centers and orientation of a joint can be keyed animatable and attached to a dependency, other than that...?

I did however see something strange in ShaneNewville's post about using magnets in your other thread, a few parameters in the Other parm group that are curious. Then again I don't use magnets very often and am only a novice Poser animator, might be relevant, might not...