From what I have gathered so far it seems that polyphonic options are limited with arduino, and I might be better looking at something like a raspberry pie.
Single sounds looks easy with arduino with some promising options but I've not found something that can play multiple sounds mixed together.
You originally asked if you could play mp3 on an Arduino and with a shield you can.
I guess what you are saying is that you may have a number of alarm conditions each of which might have its own associated sound and several of these might require to be active at the same time. Providing there are not too many individual alarms it may be practical to have mp3 files for each possible combination of alarms e.g. if you had alarms for 'fire' and 'ground proximity' you might need three mp3 files; fire alone, proximity alone, and fire and proximity simultaneous.
I am not sure how much better the Pi is than the Arduino would be for this but I don't know much about Pi and sound. If some of the alarms are spoken warnings then the problem may be similar on both devices.
There is a lot of overlap between Ardunio and Pi and often either can be used. The Pi is strong on audio visual, the Arduino is strong on hardware interaction. A big difference between the two is that the Pi runs an operating system and the Arduino does not. The absence of an operating system makes interacting with hardware simpler and more predictable.
You should probably "storyboard" the Man Machine Interface the the spaceship is going to have first and then decide whether the Arduino or the Pi is the best solution.
Sometimes simple is best. I remember playing a Lunar Lander game where the attitude and thrust of an Apollo Lunar Module could be controlled. It had a very simple interface but with a realistic response to thrust and gravity, great fun to play.