"The latest push back leaves just a week for the various mentor organizations and Google's staff to assess the student applications and marry them up with appropriate projects."

Actually, no. The ranking of applications and assignment of students to mentors by the mentoring organizations happens after the applications close. Also, Google does not evaluate the applications, that's up to the mentoring organizations.

Surely they just understand that most students leave stuff to the lass minute and constantly miss deadlines?

Not where I'm studying - unless you have a very good reason, 1 minute late and you've had it: zero marks.