HUMS in real time would not be a reality, near real time maybe and segmented data maybe but not true real time. You could have the system do some alerting to notify someone at the beach/ops center of a potential issue and may be able to do some spot or threshold monitoring but currently that would be about it.
A few other issues you would have to deal with and have been raised in other discussions is how much do you want someone from outside the aircraft making choices for those in it. Not only would you have to deal with a lot of decisions on what extent you want to go per your company guidelines you may also have to deal with government/operational area rule sets as well which may limit or prohibit this activity.
Then you have to deal with equipment. On a truck or piece of shore based equipment you have an unlimited amount of flexibility as to where you can place your antenna and the gear for the system and how it's wired up. With an aircraft you just can't do that. Not only do you have to get approval to add the gear, you may not have the proper real estate on the airframe to place it.
On top of that you have to judge satellite communication reliability. I would guess that most company's don't know what that is currently but I can tell you that at times it can be spotty and most days you will have at least 2 short periods of drop out of coverage (Iridium) . They are short but they will effect any and all data. In addition you can count on it that systems will loose connectivity and need to have power recycled and you will need a way to identify that the system is not sending data or good data and have the pilot intervention to try and correct the issue.
So a but off the main focus of the thread but some things to consider when talking about real time HUMS data.