Can late recommendation letters have a negative impact on grad school application?
Sometimes the deadlines for recommendations are flexible, and the references have some grace time to get them in.  In my department, we are certainly flexible, but we are not exactly inundated with well qualified applicants either.  I think our approach is pretty typical (at least for the sciences and engineering).  However, I have heard of higher ranked schools being more of sticklers for about the deadlines.

However, if the letter is accepted, then when it happened to arrive is totally irrelevant.  The faculty evaluating the applications almost certainly don't even see when the various parts of the application file arrived.  And even if somebody did see that a letter was late, if anyone were to be blamed, it would be the person who sent it in late, not the student who requested it.