@Blanc is essentially correct on what the integration actually does. People mistakenly think it’s DEVONthink controlling the ScanSnap (which Fujitsu doesn’t allow). The integration was DEVONthink was aware of what and where the ScanSnap software was sending scans and would import - and optionally OCR - from that location.
And for any passers-by: That location should not be DEVONthink’s Global Inbox. Using the default location suggested by the ScanSnap software is generally advisable.
D’OH! Of course, there is indeed a “Move to Trash” option in Preferences under OCR > Original Document, and I had left it deselected.
I tried selecting the option, and now the document vanishes from the ScanSnap folder once DT3 has run OCR and filed the document away.
Thanks for pointing me in the right direction, Blanc!
Just tried to scan for the first time with beta2, and DEVONthink did not automatically ORC the document that ScanSnap Home sent it, even though that setting is checked in Preferences.
I realise this is still an area that is actively being worked on; I just wanted to give my feedback!
Please see my solution for this here, maybe it will work for you: DT3b2 not performing OCR automatically
Aha, the old “wiggle the switch back and forth a couple of times” solution! 
Thanks, I’ll give it a bash!
… and, it works! Thanks!
Oooooh, is that the technical term? 