The parts on that eBay sale certainly look like the core components, however my suspicion is that (depending on what you've already got) turning those parts into a fully functional Pro satnav system in an F30/31 could be a little more tricky.
For one thing, does the car already have the correct wiring to accept the parts? Then there's probably going to be some coding involved. Finally, if you browse thru RealOEM you see various components around the car (aerials and such like
) that differ depending on whether you have Pro satnav fitted or not, so a few potential gotchas maybe.