Or is this a wrong assumption because the crossover prevents high frequency info from going to the bass and low frequency info from going to the tweeter so that each part of the speaker is doing just its part?
Yes, this is a wrong assumption for exactly the reason you state. I'm sure the tweeter on the 1.6 is not intended to run full range.
I have bi-amped with two identical amps, but not with my Maggies. I was using two PS Audio C-100s (class D amps) at the time and can't say it made any difference.