Will 32GB of RAM work on a Z370 motherboard with an 8700K processor?

Yes, no issues. That motherboard and CPU support DDR4 RAM up to 64GB or 128GB, so 32GB is well within spec. Use a 2x16GB kit or matched 2x8GB sets with correct slots and an updated BIOS. It’s a good upgrade for video editing, VMs, or heavy multitasking, but won’t boost gaming performance over 16GB.