This is a great question...it would be helpful to hear an answer even a flat out no would at least be something.
As 4D begins to gain momentum this will be a more common query/requirement.
I have just been asked the same question myself today and I am investigating whether it is possible using Navisworks Simulate (Timeliner) 2013 and also alternatively using Synchro 220.127.116.11.
I have asked the question of Synchro so let us see who is quickest off the mark! (it does not look like Synchro can 'see' the volume of a solid although ti doesn't look like Navis can either) I will post the anwser from Synchro here (I would imagine i'll have an answer in the next few minutes if my contact is able to access email)