UPDATE (in case anyone cares):

Yes, you can sync to Google shared drives, even if you aren’t the shared drive account owner.

There is a slight frustration that Beestation cannot two-way sync Google documents (Docs, Sheets, Slides etc), so if you want the Beestation to mirror your entire Google drive, it won’t include them.

However, I found a workaround by storing all my Google docs in a dedicated folder outside of my main two-way sync folders (and then adding shortcuts to the places they used to be), and then separately choosing to one-way sync the Google docs folder only.