No, we will always attempt to seat students, even those who request an exam late. Students who schedule last-minute are the hardest to make arrangements for, so please encourage your students to schedule as early as possible.
If we do not have a seat available, we will contact you as soon as we become aware to suggest an alternative arrangement. For instance, we can let you know an alternate time/day that the Testing Center does have space. If we are not able to come to an agreeable alternative, we will likely recommend that you work with your department assistant to locate a room for the student especially if the student has a reduced-distraction testing environment or private testing room (although we will try to prioritize seating these students). If a student is eligible for only extended time (and no accommodations related to the testing environment) the student can take the exam in the room with the rest of the class as long as there is a location available for the student to move to receive their extra time after the class ends.
As we assess the demand for the Testing Center this fall, onboard additional support staff, and learn more about your courses and the amount of advance notice that students are likely to receive from you regarding scheduling a test, it's possible we will be able to reduce the number of days in advance that a student needs to schedule (to avoid being considered a late request). Thank you for your patience in the meantime.