Sure, as long as you can physically connect the computers together. Some hubs still have a BNC connector on them, although BNC isn't that common anymore. You do want to do this with a network since you meantioned the BNC connector, right? If the files aren't that big you might be able to use that 'useless' floppy drive to do the transfer.
If you want to network them, you could use an old version of DAVE. DAVE 1.0 came with a StarMax computer I have, and it shipped with System 7.5. What System does the computer have?