Like has been said people used offline play to dupe items into multiplayer, am sure that Blizzard could keep them seperate so there is no possible way to transfer anything from offline play to online play.
However they've said they don't want to do this because they don't feel that forcing people to start over from scratch if they make a multiplayer character is a good idea. At the end of the day most people have broadband these days and while it really sucks if you have net problems or even no net, the vast majority of players don't have these problems.