No. People can apply late and have a late interview. People can apply early and have a later interview than those who apply late. I was 4th batch, and got my interview ahead of those who applied earlier than me. It really depends on how many interview slots they have, and who they can accomodate. Some schools invite later batches than earlier ones so that they can interview the ones that they are interested in regardless of when they applied. Some grant interviews on first-come first serve. There is some truth to what you said. If they like you, then they'll give you an interview date. However, it varies from school to school.
