General rule - if property is owned by a Jew, as is the case of just about every yeshiva that I know, then they must do bedikat chametz. IIRC, if one leaves the property more than 1 month before Pesach and will not be returning before then, no bedika is required. I can't say that this is what occurs in Israeli yeshivot. But in U.S. this is not the case, so a bedika is required.
A yeshiva down the block from me has dorm rooms. Students are responsible to clean their own rooms and share responsibility of the public shared spaces. Since they leave about 2 weeks before Pesach, they do bedika before they leave, from what I understand.
As for the rest of the yeshiva, there are public spaces used by the community all 385 days of this year (yes. The 385 is correct!) This includes kiddushim during Pesach, shalot se'idot twice this year during Pesach. I believe that the Rosh yeshiva does the bedika Erev Pesach. Point is, it needs to be chametz free.