The answer to your first question is yes. In classical adaboost, if a newly added weak learner (e.g. ClassifierB) does not reduce the overall empirical classification error, the algorithm stops. So, the linear combination of weak learners should do at least as well as the best weak learner.
Your second question: adaboost is an additive (and sequential) model. That is, the choice of ClassifierB depends on the performance of the previously selected weak learners. If ClassifierA performs badly on specific data points, then Adaboost increases their weights so that the next weak learner (ClassifierB) tries to handle them more than the other data points.