Can I run ECC RAM on a B660 board with an i5-12600K?

No. Intel only supports ECC on 12th-gen consumer CPUs with a W680 chipset motherboard. B660 boards won’t enable ECC functions, so ECC DIMMs will run in non-ECC mode or may not boot. If you need error correction, get a W680 board or a Xeon with a C-series chipset.