Regardless of the no cd thing, as long as you dont want both comps on b.net at the same time you could do that.
Yes you could essentially have both cd's on at the same time, but dont forget only one will be able to be on as the expansion.
If you have the expansion cd in, and a non expansion character then yes you could swap back and forth. But if you want to swap items from an expanded char or to an expanded char you will need expansion cd on both sides.
What I would suggest is trying it over a simple TCP/IP connection instead of going to b.net
Of course that only applies to open chars too...
SO in summary lol
If all you got is non expanded chars you're good to go (closed b.net players)
IF you're open players your best bet is for a tcp/ip connection.
b.net checks to see if your serial number is already online and if you are ... sowwy