Yes and no... not specifically a button but you can recover the previous mechanism "default state" if that is what you are looking for.
The idea behind this is that you had run a Mechanism Analysis and saved it. It can do anything, or nothing; you just need an analysis saved. From there you would Play the analysis. Slide the Play slider all the way to zero and exit. This is the position of the start of the analysis that you ran earlier.
Not elegant if you are not looking for motion, but it is the only way I have found to -reliably- reset the linked structure.
Again, I am not sure this is fully applicable to your needs, but it is an observation I've made playing with mechanisms.
Of course, limits in your constraints are the other way to avoid illogical conditions but they are not the be-all and end-all solution.
Motion Skeleton is a regular mechanism in all meanings, same way mechanism can "collapse" so MS can.
Easiest way to restore initial state of affairs is to create a snapshot right after you create your Body Skeletons.
Then whenever your mechanism (of any type) collapses to an undesired position due to high # of DOFs you can restore initial position by one button hit.