I'm far more worried about the obvious cliff of degradation that will occur to match quality coming with the free week. As you say, the cheaters will come out in full force and make the game as unplayable as redsuck currently is.
Aside from that though, I think it may bring back players who refunded but still have an interest in BF6 so long as it's good. They're really putting all their eggs in to one basket by making the free week patch week. Honestly, they should have released the patch, seen how it actually works (I'm betting server crashes on patch day) THEN done a free week so long as everything doesn't explode.
I want the game to succeed and get more players. Free weeks can bring in more long term players... providing they like their experience.
Guess we'll see...