No. The motherboard will never function, as if there is a different CPU installed. It will only boot, if it recognizes the components that are installed.
Check your motherboard vendor for a compatible CPU list.
The Core 2 Duo E8600 is an ancient LGA 775 socket. I have no idea what Celeron you're talking about. All the recent models would be LGA 1151 sockets, and in no way are compatible.