The chances of getting an offer are much higher in Ivy schools, that's true. Most of my friends at Harvard had 2-3 MBB offers without investing too much in prep. I know that in non-Top schools getting an offer was quite challenging.
But on the bright side - its possible. You should invest a lot in prep, ideally even before starting your MBA. You'll not have time for prep during your MBA
One important tip - your classmate (ex MBB) should refer you to the on-campus MBB recruiter to make sure that you get an interview invite