Correction to Voltronic, the word you are looking for is "truncation" (discarding excess bits), not "decimation" (which is a step in sampling/resampling)
If I'm recording at 32-Bit, and then downsample to 24 or 16-Bit for distribution, will that introduce clipping because of the limitations of those 2 bitrates?
As commongrounder mentions, what you describe is not resampling, but a
truncation of bit-length or bit-depth. That is to say, a lopping off and discarding of the least-significant bits.
Doing that
can introduce clipping (or noise), but won't if you do it correctly. In essence you are moving the content from a very sloppy fitting larger "container" to a better fitting smaller one. So yes, you need to make sure it fits.. AND is positioned correctly inside the new container.
As covered in many of the discussions here at TS about "32-bit float recording", not only will all of the live music recordings we make already fit comfortably within 24bits, anything that can possibly be recorded successfully by any of the 32-bit recorders folks are currently using will also fit in a 24-bit "container". The musical content itself and everything we want to hear will always fit within 24bits.
However, because 32bit recording (or more accurately, the auto-switching ADCs schemes used in "32-bit recorders") delays the need for proper level setting until after the recording has been made, that musical content is likely to be shifted way up down in level, so its level needs to be adjusted prior to listening and/or conversion to a 24 or 16bit file format. Normalizing is the "doing the level setting afterward" part. There is no need to try and push it as close as possible to the limit by normalizing the highest peak all the way to 0dBfs. It's safer to normalize to a little less. The exact value doesn't matter. -1dB or -0.5dB is fine.
The next step after normalizing is the bit-reduction truncation. Whenever bit-reduction is performed it is always best practice to add a bit of dither (random noise) at a level just a tiny bit louder than the truncation value. Doing so essentially "smooths the sharp edge of the cut" eliminating quantization error. Even though that error is very low in level and probably not audible at all in a music recording, if made loud enough to be heard, quantization error noise sounds terrible, so a tiny bit of very low level random "hiss" (dither noise) is preferable. It may not be absolutely necessary to dither when reducing bit-length from 32-bit floating point to 24-bit fixed, in the same way that its not technically necessary to do so when reducing to 16-bit, but it is still best practice. So.. always dither whenever reducing bit-length. Its easy enough to do the right thing (usually by just checking a box to apply it). Don't worry about fancy noise shaped dither. Standard "triangular dither" (TPDF) is fine.. and is preferable if further processing might be done.