Eli Rosenbaum at the Washington Post says no: "In practice, such commissions have not been nonpartisan, apolitical or effective."
We do not entirely agree with that -- they have been highly effective in Canada. But in the USA, it looks like Rosenbaum is correct: he cites Arizona, New Jersey, and Washington as the 3 states with such commissions already with more than two House districts. And as you can see by clicking the links to their district maps, all three look pretty darn gerrymandered, with Arizona being especially blatant, but the other two still seem fairly clearly gerrymandered. (Do you like the two "go out to sea and come back to land" districts in Washington?)
"in the past two House election cycles, every incumbent in New Jersey, Washington and Arizona won. "
"as the current commissions demonstrate, equal representation on the panel for both parties tends to favor the status quo. The commission is indeed bipartisan, not nonpartisan, and each party's delegates on the panel are closely connected to their state parties and politicians. To avoid gridlock and approve a plan, commissioners must draw a map that is pleasing to both sides, and of course nobody on either side really wants a competitive district. Political scientists even have a name for this type of redistricting scheme: bipartisan gerrymandering."
"In New Jersey, the commission worked closely with the state's congressional delegation, even scrapping one proposed map because it failed to win the support of key Democrats."
Even worse, Rosenbaum argues, should such a commission produce unfair or unsatisfactory results, voters have no recourse.
In view of this, it seems to us that the non- or bi-partisan commission "solution" is not as good as our own algorithmic solution.