Yes, that's the idea. At least in the place I live, you just need to go to a convenience store, tell the cashier the phone number and pay cash.

again, once you pay for it, even with cash, they can track you down(though it may take a while). It's trivially easy to see where a given # is, so once they know the phone #, they can pretty easily find out who has it in their possession, by just showing up and seeing who has it in their hand.

Not to say there isn't SOME anonymity by paying cash for a burner phone, but it's not even remotely fool-proof for anyone really wanting to figure out who you are.