Yes. Staph is a bacteria that is spread on contact. If it reaches an open area on the skin it will thrive and grow. Handwashing, treating the infection with antibiotics/topical cream and keeping the infected covered are ways to reduce transmission from one person to the next.
To my knowledege staph infections are contagious. Look up on the internet. She could ask her doctor. He should know what kind of staph and wether or not it is contagious.
Unless there is exudation (leaking of fluid) the liklihood of transmission is virtually non-existant. If there is an open wound, normal hospital precautions will make transmission of the organism unlikely. Bear in mind that the organism itself is found everywhere, from restrooms in gasoline stations to the floor of a city bus. Generally speaking, transmission involves skin breakage and bacterial contact with circulating blood and a co-factor of a depressed immune system.