No, it may be just a memory address like any other (it can also be a register or other special address). The reason it's a problem in normal programs is because there usually isn't code there (and with memory protection, you probably aren't allowed to access that space, which is the error you often see).

The CPU doesn't care if the address is all 0s, that's not special to the CPU. So when it turns on it just starts executing at some hard-wired address. That could be 0x0000, 0x8000, or it could be something really random like 0x48C4. Somewhere in the chip's documentation it says what the address is. Once the CPU has power, it loads the first instruction from that address, and then it executes everything as normal.

So you wire up the computer so that some little piece of ROM (for example the BIOS) sits at that address. When the chip turns on, you know what instructions it will start executing.

Once things are going, you could set things up to be more complicated (such toggling pins to signal the ROM chip to stop listening so you could map normal RAM into that address), but that's the basic idea.