If a staph infection entered your body through a small cut, would it cause a skin problem (boil) or immediately poison your blood (bacteremia)?

Boil over bacteremia. For a bacteremia to develop, things have to be pretty serious. That said, I respect Staph aureus very much-it's a very nasty, dangerous germ. Most likely the scenario you describe would result in a small localized infection- a boil or something of that nature. For the 'extra step' of the bacteria entering the blood stream, there has to be several factors involved - the germ itself, host conditions.