Yes, and no.
If you really need an assembly, you'll have to export each part as a parasolid (or some other neutral file), import each into 2006, and re-assemble.
If you just need a representation of the assembly, you can save the 2007 assembly as a 2007 part and then export this new part as a neutral file which can then be imported into 2006.
As far as getting native data back a release, you're SOL.