Is the coolant system supposed to suck coolant out of the overflow bottle, if it needs it? If so, them what would cause it to not suck coolant from the bottle?

 

A bad radiator cap.

 

or water pump

 

here is what happens....
when your car builds up pressure in the coolant system, the pressure pushes the plunger on the radiator cap.....the plunger will then no longer block the hole going to the overflow tank and pulls or pushes the coolant into or out of the tank......if your not getting the coolant back then it is a bad cap or a non efficient water pump