They probably won't, and the reason for that is the fear that pedophiles will use it to prey on young children. As it is, there was some newapaper who published a very ignorant article which said there was a danger with Pictochat being used by pedophiles as it is, even though you have to be within 30ft of someone anyway. The newspaper didn't didn't do their research, and they were wrong, but now imagine if Pictochat really was online capable. Then their fear-mongering would at least have some merit.
I suppose it is possible they will do it, though, but if they do you can be sure it will be loaded with filters and parental controls. I also don't think it is possible to update the firmware in the DS, so if they were to add that it would have to be in a cart or card which you would have to purchase separately. But that rumor of a new DS revision is exciting, and I'm wondering if we might not see it in that new model, if that rumor is true and if it ever actually materializes.