That depends on what BIOS you now have installed.
ASUS site says the FX-8350(FD8350FRW8KHK,4.0GHz,8C,125W,rev.C0,AM3+) has been supported since BIOS 1201.
ASUS site:
M5A78L-M LX PLUS supported CPUs
You might be able to update the BIOS from a USB device but you won't be able to find and download it if you don't now have BIOS 1201 or later installed once the fx 8350 is installed. I would download and install it with your current processor and then swap the processors.