You know would this result in permanent Dem control of the House?
First we get 53 black seats. Then probably around 12 or so of the 16 Asian seats. Probably all of the AIAN seats, plus the HIOPI and Other seats. The White + Asian seat might be competitive, but not the rest. That's already about 70 seats. Then with his Hispanic seats we probably take about 48 or so out of 55 (conservative estimate, I'm giving them about 3 Cuban seats and maybe 4 or so scattered ones around Texas and the west) and probably end up with close to 110 seats. We need barely over a third of the White seats.
"Democrats only need to win a third of white seats" is looking at it the wrong way, since it's easy to think they could in the abstract (but they're probably unlikely to).
The main effect is pack mostly heavily Democratic voters. That is a key aspect of a pro-Republican gerrymander. The only situations where it could possibly be beneficial to Democrats is in the Deep South, but even there the extra black majority districts are probably canceled out by much reduced capacity to elect white Democrats. McCain won the white vote 55-43 (and Bush won it 58-41 in 2004) so that translates to over 70% of white seats in a close election (based on the
cube rule). If that seems off, take a look at a bunch of Democratic-leaning congressional districts and think what would happen with all their minority voters subtracted. (For instance, McCain narrowly won New Jersey whites).