I found a partial answer in this article on the smaller and younger Giordano Bruno crater.
The impact creating the 22-km-wide crater would have kicked up 10 million tons of debris, triggering a week-long, blizzard-like meteor storm on Earth...
So the secondary effects of the Tycho impact would have been even more spectacular. However, I don't know whether the fragments would have been large enough to devastate the Earth's surface.
Experimenting with an online impact simulator it appears that the Tycho impact was somewhere in the order of 1.00x10^23 joules, judging by the size of the crater. This is about four times that of the G fragment impact of Shoemaker-Levy 9. When you consider all the fragments it would be fair to say humans have witnessed an impact of similar magnitude to Tycho.
