This may be a bit late, but give the following a try.
[ol]
[li]Open the assembly.[/li]
[li]Use mass properties to find its volume (assembly volume). I ran a simple test and it looks like this volume is the sum of the component volumes, and does not take overlap into account.[/li]
[li]Save the assembly as a part, with the all components option selected. This generates a part with a solid body for each of the components.[/li]
[li]Create a solid block large enough that the assembly would be able to fit inside it.[/li]
[li]Use mass properties to find its volume (block volume).[/li]
[li]In the block, use insert part to include the part version of the assembly. Position it so that it falls entirely within the block.[/li]
[li]Insert a combine feature and select subtract. Use the block as the main body and all of the bodies of the inserted part as Bodies to Subtract. Keep all of the bodies.[/li]
[li]Use mass properties to find the new volume (new volume). [/li]
[/ol]
block volume – new volume + assembly volume = total volume of overlap
To narrow it down further, you could write a macro which subtracts the solid bodies one at a time and compares the decrease in the block’s volume with the volume of the subtracted solid body.
If you have access to the mold design tools you might be able use the cavity tool to accomplish the same thing without saving the assembly as a part.
Eric