It's not about your speaker output, it's about your wav file outputs.
32 bit is significantly better than 16 or 24 bit, not merely because it has a better noise floor (which is why 24 bit is better than 16 bit), but because it is floating point instead of integer.
What this means is that it uses those bits more flexibly to differentiate your points, but really, even 24 bit is more than the average human can hear. However, when you are still working on your tracks, 32 bit also can safely go over 0db without clipping. What I mean is, the numbers will go over 0. This will still sound like crap on a sound system, this is not what you want as your final output, but while you're still working, it's beneficial to have it so bouncing your tracks to wav doesn't kill your track if you accidentally clip.
When you're ready to save down your master, you're probably going to want to export it as 16 bit, but until then, yeah, keep your wavs as 32 bit and you absolutely want your internal mixing to be 32 bit. It doesn't matter AS much for your recorded tracks, but unless you have a serious disk constraint, it's still worth just keeping it the same as the rest of your chain.