A nice idea, Jerry, but a couple of factors may have stood in the way of the kind of merry-making you suggest.
Firstly, I wonder how much an up-to-date Victrola cost in 1912? Bob Godfrey can doubtless provide us with some figures and then set the price into a period context. If I'm right in thinking they were prohibitively expensive, then they would be out of range for most second and third class passengers.
Then again, as you observe, the Edwardian rich were not noted for their habit of travelling light and they had ample means besides to indulge their whims and fancies. Maybe they WOULD have lugged a gramophone with them on their trips abroad...I'm smiling as I type this, recalling the haunting opening lines of 'Out of Africa', narrated by Meryl Streep and set in the years immediately before, during and after the Great War:
'He even took the gramophone on safari. Three rifles, supplies for a month and Mozart'
As you can tell, I've watched the film many times over!
However, I think it is unlikely that any passenger would have played their music in a public room. I'm guessing that our great-great-grandparents had more consideration for their neighbours than to inflict their tunes upon them. I myself start foaming at the mouth whenever I'm forced to listen to rap or hip-hop or some similar musical excrescence, blaring out of some oik's mobile phone or MP3 player, on the Tube or bus or wherever. Besides, the ship's band would have provided LIVE music, either for ambience or for dancing, at various times throughout the day and I gather that their repertoire was fairly up-to-date. This was surely better than the tinny, scratchy sound of even the best gramophones.
But...who knows? The private promenade decks of the de luxe B deck suites (occupied by Ismay and the Cardezas) would have made delightful venues for informal tea-time or evening dancing - not least, because space in the staterooms and sitting rooms would have been too limited for more than two couples to take to the floor at any time.