That would be neat trick, since there was a lot of wood in those things. Probably not much left.
Not sure I agree with going into the wreck to retrieve artifacts; it's like robbing a grave. 500 years from now is one thing, but it's only 108 years ago; I wouldn't be too thrilled with someone digging into my great-great-grandparents graves to poke around for artifacts.
Going in to do nothing more than take photos to aid in creating an accurate recreation would be OK.
While it might be a cool museum piece, I dont understand the reasoning for spending the couple hundred thousand dollars or more to make this happen. But on the flip side. I see why they would want to try to save some pieces, before it is completely lost to Davy Jones Locker. I think there wouldn't be too much left of the original radio after all this time either.
For a whole lot less money you could visit the Titanic Museum in Belfast and see reproductions of the ship including the radio room. One of the problems in 1912 was that the radio room was owned by Marconi for the purpose of making money transmitting telegrams for passengers. Ships of that era did not maintain radio watches for the safety of the ship. They were private for profit operations. Of course, that changed after the Titanic sank.
The American Museum of Radio and Electronics in Bellingham WA has a recreation of the Titanic's radio room, with contemporary furniture and electronics. Why anyone would spend so much heaving a heap of eroded and useless material from the depths is beyond me. Go to Bellingham.