Actually, while that might be a generalization, I know that there are exceptions. I have worked with a few computers in the hardware lab at my school where there was no CPU present, and the computer would power on (no speaker so I don't know if it gave beeps). The fans whirred, but nothing more (obviously). The same is often true with a dead CPU on some motherboards.
Having nothing connected will not damage in any way, shape or form. It's actually good to do that for troubleshooting purposes. Whether or not it will power on depends on the motherboard itself, but in most cases, johnjkr would be correct.
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