Hi there,
yes this motherboard will run the 3570k but as you have read it will need the F10 BIOS to do so.
Bad news is that you will probably need a supported Sandybridge CPU to update the BIOS if it doesn't come with the F10 and the only way of discovering this is to try it with the 3570K. This won't harm the board, it just won't start if the CPU isn't supported.
And the answer is no, you cannot flash the BIOS without a supported CPU mounted.