No, the Firehouse 5 tracks play on the Mark Twain. A friend and I were just discussing this. Here's what we figured out. paraphrased:
A) Dock depature
Jazz:Fire House 5:"Millenburg Joys"
B-1)Frontier tune: name unknown
B-2)Frontier tune: name unknown
B-3)Frontier tune: "Western Saloon"
C) Dock arrival-exit
Jazz:Fire House 5:"Come Back Sweet Papa")
The above all played on board the Mark Twain. There was also a D) Dock Music.
There was also a sad-slow track that was the "hold" music on the boat when the exit/load took a long time----this was used at least untill the early 90's. This is the track which underscores DLP's Molly Brown(or Mark Twain or possibly both). Those B tracks 1-3 are also used with two others at WDW- they were recorded at the same time. I assume since WDW doesn't have new Orleans Square the 2 Jazz tracks Disneyland uses are replaced with 2 additional Frontier tracks. That B-3 track is a version of the track "Western Saloon" that was once the Disneyland Frontierland entry stocade music---WDW's Frontierland used it in part of there Frontierland area tracks in the 70's & 80's. The track was from The Capitol Records media music series-I've even heard it on Rin & Stimpy.
The above all played on board the Mark Twain. There was also music that played only on the Dock. The Dock music was live with a real band organ in the passenger shelter --- they use a recording of the machine at the passenger pens----in the last year I've heard it playing a few times-most of the time now there is no music----------The passenger pen used some banjo tracks at one time.