There's a theoretical advantage to using 32-bit in Cool Edit, and a practical one.
The theoretical one is that, just maybe, you could do enough processing so that the dither noise (added repeatedley at the 16th bit) could become audible. You'd have to do a lot of processing of some very good vinyl, but many people claim to hear a difference. I'm not vonvinced. It's very slow using 32-bit compared to 16-bit.
The practical advantage is that the 32-bit processing in CE gives (at least) 24-bit accuracy, but with floating point processing. This means that, once recorded, you don't have to watch the levels while you're processing. Your sound card is limitted to fixed point (16 or 24 bits) so at play and record you have to be careful not to clip. But the actual 32-bit processing within CE cannot clip, and does not have a lower limit either. So you can neither distort the signal, nor push it down into the noise.
If, after processing the signal does go above 0dB FS - just reduce the level - the signal is still intact.
If, after processing, the signal is way too quiet - just increase the level - there's an (almost) infinite amount of low-level detail, all stored to 24-bit accuracy.
If you don't believe me, use the 32-bit mode to try boosting or cutting things by 200dB - they survive perfectly. Now try it at 16-bit

You may think that the added luxury of not having to "watch the meters" makes it worth using the slower 32-bit processing. Personally, I (usually) don't, though it's sometimes useful.
You still have to watch the meters on record, and if you play back audio that's over 0dB FS in the 32-bit domain, it'll still clip in the 16- or 24-bit domain of your sound card. It's just the processing that doesn't suffer, meaning you can always correct any clipping you create, without undo/redo.
Cheers,
David.