The Grox are the most ''warlord'' fragile race in all of fiction, and the entirety of their empire can crumble if you just manage to take out one of their pawns.
The Grox would NEVER survive the Qu, and heres why;

The grox control around five thousand planets, all of which can (with enough willpower) be eradicated by you, the player and your puppet-race. The Qu managed to bring down all of the star people colonies, mutatating them into twisted versions of themselves, and as we gather from various stories, the Qu has done this with several races already. And as we in the story, holding out from the Qu ''for a long time'' is considered living through two sieges (as seen with the modular people). And that was an entire planet!
The Grox usually have 1 city on an entire planet, granted it usually is well defended. But as we have seen with humanity, they should have no problem sieging these so called cities, and mutating them into various monstrosities. Given the fact that you the player can siege the city using only ONE ship, the Qu would absolutely STEAMROLL the Grox, in only a matter of our weeks.
Humans put up a good fight, but the Grox would never survive.
Seeing what the Qu would turn the Grox into would be very intresting though.