Since there's no way to use a TCP/IP stack through a serial connection (at least not this way), there's no point. You could use an adapter like this to talk to BBS software running on the Amiga through ethernet, but you can't actually open outbound connections.
It's similarly slow and much more feasable to run a serial cable to another networked computer and set up the latter to share the connection (PPP server). On the Amiga you'd set up a PPP connection (like w/ a modem, just without dialing) and off you go.
