If you are allergic to yeast then yes it is possible to experience break outs, however generally yeast allergies have other symptoms and occur after eating breads, beers or wine.
Yes it can. It has happened to me. This happens because your body may be intolerant to yeast. I would recommend you go to a nutrition doctor and test for your blood type. Intolerance for foods causes skin reactions such as acne.
Yeast makes the pimples or acne to rise out faster and having them leave your skin which will help you long term. But you will have to keep your face clean.