The Application deadline is somewhere between October 15th to 30th for most schools. The process is that one files the AAMCS application, defines which schools to apply to or wait for MCAT score to figure out the choices. The schools need to provide their secondaries to be submitted and one has to write those essays.
So you are essentially playing with one week spare time and pray that all stars are aligned for the perfect timing.
None of that guarantees that any interview slots are left over by the time your applications meets the exact deadline.