I would say: yes it was. Until now, probably the only ship in history.
Throughout maritime history, many ocean liners hired musicians and bands to play for the passengers
This is not entirely correct. "Throughout maritime history" creates and impression of an age old tradition. In fact, passenger transport only became important cargo after the invention of the steam engine. And yes, passengers are technically a form of cargo. Often jokingly referred to as 'complaining cargo'.
Before that, ships did carry passengers, but only in addition to other cargo. As far as I know passenger sailing ships did not exist. On shorter routes, possibly. Definitely not on longer routes such as the Atlantic crossing. Even Channel crossing were not done with dedicated sailing ferry ships, but converted fishing ships until steam engines became reliable enough.
Ocean liners are ships dedicated to the transport of passengers (cargo is an extra) on fixed routes. That became only possible about 100-120 years ago when steam engines became reliable enough and ships safe enough (less dangerous is probably more apt). Before that period (around 1860-1880) ships may have had a few cabins, but were still cargo carrying ships with additional accommodation for a few passengers.
It's not just the reliability of the engine and ship that is important here, but also the size of the ship. Ships before the 1900's simply weren't large enough, with very few exceptions.
A band is a luxury only affordable with economy of scale. A small/medium sized ship cannot afford to waste that much space and crew on entertainment. Today - I kid you not - some cruise ships operating in the Caribbean are equipped with an ice rink and a zamboni. I watched Holiday on Ice on board the Rhapsody of the Seas. Those ships are among the biggest afloat. Only the largest ships could and can offer such entertainment economically. Back then a band, today ice rinks and a whole range of other luxuries. The Queen Mary 2 has a magnificent planetarium, for example.
Some ocean liners did have bands om board, but definitely not all of them. You have to look for the biggest liners competing for the Blue Riband, from the 1907 period onwards. Other and/or earlier ships had almost certainly no band on board.
I don't know of any band playing while the ship went down other than the Titanic. It was definitely not a tradition. Usually the band members have other things on their minds. Such as saving their lives.
Note: I talk about dedicated passenger ships known as ocean liners. Of course people crossed the ocean before the advent of steam power. Otherwise America couldn't have been colonized. But those immigrants didn't do that on ocean liners. They either chartered an entire ship, or booked passage on a cargo ship going that way. Often they had to provide their own food and bedding. Sailing ships were not equipped to carry passengers in cabins. Only very important persons would take over one or some of the officer's cabins. Everybody else had to bunk down wherever convenient.