Yes, the MultiClassClassifier turns a multi-class problem into several binary-class problems. By default, it uses the one-vs-rest method. However, it can also optionally
(a) perform one-vs-one (aka pairwise) classification (and, with a further option turned on, pairwise coupling), or
(b) use random error-correcting output codes, or
(c) use exhaustive error-correcting output codes.
In each case, binary classification problems are created. You can look at the classifiers that are generated in the output (assuming the base classifier is a decision tree or something that has a nice printable representation).