You could use a different technique to determine clearances. I might suggest assembling the object twice. During the 1st part of the simulation, you move the robot without the object. Once the object is grasped, you switch the display to the other object that is constrained to the robot. Now you have 2 simulations but the end game is the same.
When I did a radial ball bearing, I thought I could simply tell Mechanism that a ball was rolling between two concave surfaces. If I held the inner race and applied a servo motor to the outer race, the balls would roll at their appropriate rate. After much fussing with constraints, it was in fact an exercise in managing gear ratios, which is what I wanted the contact surfaces to deal with, to finally achieve the "analysis" I wanted to obtain. Problem here is that by the time I had "programmed" the "problem", I already had the answer in my notes.
Also look at the motion envelope feature. This feature makes interference analysis much easier.
The other side of this coin is normally presentations. Again, you can splice separate motion analysis together to follow through on the two unique states.
Even if you have this model as interactive, simply switching visibility of one of the objects will still achieve your goals. However, if the means is the critical objective, then again, I too would like to know if there is a better way within Mechanism... and to know if the premium Mechanism extension is required or even capable of achieving your goal.
