Chris, the question isn't really whether or not the ship can be raised. The technology is certainly within reach if it doesn't exist in bits and peices already.
The question is; Why bother? It's not for nothing that salvage is termed a good way to turn a large fortune into a small one.
A very small one!
Nobody...and I do mean nobody is going to make the enormous investment in manpower, materials, ships, equipment and money that would be required for such a project unless there's a reasonable hope of getting a decent return on the investment. That's just not going to happen with a gutted shell that's been underwater for close to 90 years, the costs for which raising and conserving would be staggering.
And what popularity? Outside of the communities of liner researchers and maritime historians, you would be amazed at how few people know the Britannic even existed...much less even care. In any event, since the ship is registered as a war grave, you can bet that your chances of even gaining all the permissions needed for such a project are so close to zero that the difference isn't worth mentioning.