Will a PS3 work without a hdd?

May be...

An auction for a ps3 states that it will not work without it. Will it still turn on? Where exactly is the system's OS located?

If your getting a good price buy it because you can just buy a 320 gb hardrive for about 60 dollars which will store like 100 games

The operating system is stored on the hard drive or the HDD. You need one to do anything with the ps3. If it doenst have one it better be a decent deal you can buy a 500gb for about 110. But ask the seller why no HDD. There might be a story behind it. But if everything checks out get it if its a good deal. And put in your own HDD.

Um, yeah. I would probably stay away from a PS3 that comes without any HDD.