Can two computers on the same LAN share a ScanSnap by itself or through DEVONthink Pro Office?
This is highly unlikely unless you get one of those new routers (forgot which company) that allows you to share a lot of USB devices over the network. But DEVONthink Pro Office doesn’t know anything about the scanner so we can’t do it.
You could scan into a folder that you share over the network and pick up the arriving PDFs from the other machine, e.g., from DEVONthink Pro Office using File > Import > Images (with OCR)