No you need to download all data first so you dont have to trust other nodes that their data is correct. Once you build your database you dont store the blocks though.
So let me get this straight, you download all data and verify it after which you can choose to store X amount of GB and relay only that data to other nodes? Initially I thought it was going to work differently, but this does make more sense if it is the case. I haven't done enough reading recently and I'm sure that many understood the concept differently.
Update:
Understood, thanks.