Will my 3200MHz RAM work on a motherboard that only supports 2400MHz?

Yes, it will work — it’ll just run at 2400MHz instead of 3200MHz. The motherboard and CPU set the speed ceiling, so the RAM automatically downclocks. You can try overclocking via XMP/DOCP in BIOS, but it’s usually not stable if the board doesn’t support the higher speed. Don’t pay extra for speed your motherboard can’t use.