I cannot be 100% sure but it should. BIOS updates are "usually" to allow support for newer processors. If it doesn't support the processor with the BIOS it has it should still run it just won't run at perhaps the correct speed and will not correctly identify the processor. But it should still run.
You already have the board and have bought the processor so once it arrives all you can do is try it.
I would not worry too much about it, you will be able to boot up to the OS CD and install your flavour of Windows with the current BIOS version and even though you may not be running at 100% full performance with your chosen CPU, once you are up and running in Windows you can if needs be organise to upgrade the BIOS code from there
I haven't done this myself which is the reason I am not 100% sure it will run ok. But I have seen lots of posts over the years from people whos motherboard won't correctly identify a specific processor or whos processor runs at a slower speed and the solution was to flash the BIOS to support the new processor.
You might be pleasantly surprised and find its the latest BIOS anyway and might not need to do anything at all.
Do be careful. I have never had a problem updating the BIOS but be sure you have the correct BIOS download as if you do flash the BIOS and something does go wrong you will effectively kill your computer.
I'm sure this won't happen, as I said I've never had a problem but I have always double checked everything before going ahead.