Yes, you can export the pack from the iPad version of Soundbox and transfer it to your computer.
Then, drag'n'drop the Soundbox Instrument into Soundbox to install it, or click "Import Pack" through the presets manager.
Does this also unlock the editor in the desktop version?
No. Although any pack can be loaded into both the iPad and desktop versions of Soundbox, the editor can be unlocked by making a separate purchase of any Audiomodern Soundbox Instrument.
Soundbox Instruments can be found here: https://audiomodern.com/soundbox/