Skylake chipset based motherboard may need BIOS microcode update to support 7th gen "Kaby Lake" CPU, but there are some MOBO manufacturer that supports it out of the box. If your motherboard supports it, yes you can use your G4560, if not then you will likely deal with blank screen or even not booting at all. And the crucial part of computers and its activity is CPU, so flashing your BIOS needs CPU.
The best solution possible is:
Go get yourself a Skylake CPU and flash the BIOS for Kaby Lake.
You can buy the cheapest Skylake or borrow your friend's CPU.