You don't have to take them. It's perfectly normal to take a day or two or even three to start your period on the sugar pill week. Your body has to react to the lack of hormones.
So do the sugar pills even do anything? Like do they notify my body that its time to menstruate or am I better off not taking them? This whole thing is sort of worrying me.
They have nothing in them as they are placebo pills. They're just to help you keep track of when to start the new pack. You can choose to take them, not take them and throw out one each day to remind yourself, or not take them and throw the pack away and remember your start day on your own.
Some placebo pills do have iron in them, but either the birth control will have "Fe" (chemical symbol for iron) in the name or will note somewhere on the packaging or inserts. Mine do, but I don't take them as I generally get enough iron on my own.