Late Application to MSc Programs in Finance

Quick question, is there any point to applying for b-schools in their last enrollment period? Most of teh schools I'm thinking of applying to have deadlines of June 5th or June 15th but I'm assuming most of the classes have already been filled. Is there any way to figure out the availability of programs? I know LSE has an availablility section but HEC Paris, Cass and IE business school don't seem to have a similar application.

thanks in advance!