That is likely going to be a big fat NO. Understand each platform's storage servers operate on a totally different architecture and likely a totally different database back end. That means that the characters cannot be shared or transferred across family lines (PC<>PS, PS<>XB, XB<>PC). Plus both Microsoft and Sony specifically requested this NOT be an option for this game to lock the players into whichever specific model.
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That's not likely true. Most data is stored via systems like sql. How they access them may be different but a database server is a database server. It could easily be done the question is will they? As someone that owns all the platforms listed for D2 I would be more then willing to Shell out damn near $200 to own it on all platforms on day one if I can play the same character on all of them. It's easy to lock out the PS4 exlucives. It would be stupid to force players to have 3 accounts.