Replacement MCU

Can I take the Decimilla, drop in an ATMEGA8-16PI I have lying around, program the bootloader with my AVR ISP programmer and start using it as an original Decimilla?

I don't think so.
To use diecimila board with Atmega8, I think you must burn a different bootload: "NG or older w/Atmega8".

But wait for experts opinion.

You will need to burn it with the NG or older w/ ATmega8" bootloader, but it should work. Just be aware that there will be a longer delay after your board resets or a sketch is uploaded before the sketch starts to run - about 8 seconds.