I doubt you'd find any improvement in quality by rendering at 32 bits rather than 24.
The bit depth is about the dynamic range of the sample. The full explanation is complicated, but basically it's about how great a range of volume it can reproduce - the loudest it can get compared to silence. A higer bit rate not only handles a greater dynamic range but also has greater range above the noise floor the electronics invilved generate.
16 bits is around 96dB give or take, 24 bits 144.5dB, 32 bit 193dB. 16 is CD standard because when the CD standards were drafted it was thought adequate and was a big improvement on most vinyl. It can't handle the full dynamic range of quite a lot of instruments, such as the transients from drums and banjos or amp volumes when close-miking so to handle the signal peaks means reducing the volume of the sound before it hits the analogue/digital 16 bit convertor. Which means a loss of dynamic range in the recording and consequently a higher noise floor.
24 bits can handle pretty much everything from silence up to the point that if sustained the volume would really hurt a lot and make you deaf incredibly quickly. As in seconds rather than minutes. It handles all real-world situations fine, and when dithered down to 16 bits starts with a lower noise floor which is reflected in the 16 bit render.
32 bits gets you 193dB.
32 bits and 64 bit have their uses for carrying out calculations with minimal information loss but there's no reason at all to record or render at those depths unless you are close-miking a nuclear bomb test.
Incidentally, there may be a few audio interfaces around that work at 16 bits, but just about everything from on-board sound chips through RME and Apollo through to the really high-end works at 24bits. So even if you render at 32bits when listening to the result you are hearing it after your interface, its driver or maybe the software playing the file has reduced it to 24 bit anyway.
Wiki has good articles on audio bit rates, signal to quantisation noise and all the gory details if you want to look them up.