Hard to say until it's actually released or you find a reliable benchmark that states how it updated the BIOS for your motherboard. It may be that you will be able to, but if not, you might want to scope out local computer support shops to see if maybe they'll do it for you free of charge (or nearly).
Looking at the current CPU Support List for that board, it shows the Intel Celeron G440 as compatible with the default BIOS. Currently, that CPU goes for $41 shipped from Newegg. If the local shops can't/won't flash your BIOS for less than that, I'd consider ordering a G440 along with your 3770K and then putting the G440 up on E-bay.
-Wolf sends