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I think it really depends on the school. Did you interview? Does the school require interviews?
Also, some schools are really swamped this time of year and don't have adequate resources, so applications that are "incomplete" are not dealt with until after the deadline. In other words, if an admissions office has misplaced your transcript or GMAT scores or recommendations, they'll throw your app in a pile of incompletes and look at them after the notification deadline.
I'm basing what I said above on a couple of different friends' experiences with schools ranked in mid 30's, not top schools.
I'm in a similar situation. My guess is the late notification will not affect admission, but it will affect any kind of scholarship money. Most schools seem to give the money out first and then fill out the class.