Arduino 1 can somehow support 32-bit audio?
First of all,what is the point of this? I'm afraid this is a XY question. You won't get that good of quality with Arduino. If you're hoping to create some sort of an amp, learn electronics and do that directly. Maybe you should just send data via serial.

Anyway, that aside, here's a chart I drew:


(Excuse my poor image alignment, PowerPoint was being a little mean today)

The bottom is all the "channels" the PC can send. The top is all the "channels" the Arduino can recieve. As you can see, there's a huge degradation in quality. Not to mention, I made this that 1 bit = 1 "channel," yet it's very much more than that.

A standard Arduino (Uno, Leonardo, etc.) has a 10 bit ADC that can read values 0-1023. The computer can output 0-4294967295! (It' exponentially grows due to permutations). You can see why I very much simplified my chart! :P

DSP won't really work well, unless you are trying to do some weird alien sounding modifications or a cheesy echo to. You probably will want to add an external 32 bit ADC. I would recommend, additionally, adding a Due or Galileo that can process 32 bit integers without emulating a bigger chip, thus greatly reducing performance and giving you a low framerate.

tl;dr: It'll work fine, but it'll have horrible sound quality. You can't send the same 10 bits until 32, since the computer changes that 32 bits into a voltage (sent to Arduino), and the Arduino translates that voltage into 10 bits.