The Claisen condensation is rather esoteric. You definitely don't need to know it by name. (In fact, very few orgo reactions must be known by name for the MCAT. Usually you get the name and a strong hint, like reactants and products drawn out.)
However, I wouldn't be surprised if it were a step in a synthesis in a passage.
I could imagine an MCAT question like this: "Step 2 in Figure 1 involves a Claisen condensation. Step 2 takes place at pH 13. What would happen if this step were attempted at neutral pH?" That would be a hard MCAT question, but I could certainly imagine it. They might make it easier by making 3 of the answer choices really stupid, like "the reaction would change from nonspontaneous to spontaneous". The correct answer would be "the Claisen condensation will not occur at pH 7".
I have seen some very esoteric orgo reactions appear on MCATs (both the real one I took and the many AAMC practice exams), but usually you don't need prior knowledge of the reaction or mechanism. You just need some intuition about steric hindrance, and electronegativity, and the relative pH of various functional groups, and stuff like that.