Very very occasionally, but in this particularly situation it would be madness to do so.Honestly, for the number of times wolves play this card, has it ever actually been the case where an outing was faked by wolves. Not counting ones way before the deadline.
By the way, time to think about pack composition:
1) We know there is another pack. I will assume there aren't 3.
2) 3 are dead from one pack, none from the other.
3) With two packs, and 21 players, you'd expect 1/3 baddies. Most clean, symmetrical set-up here would be 3 baddies in each pack, and a sorcerer or unattached cultist. However, they could be slightly unbalanced.
Either way, with only 12 players left, I think we're up against a pack of around 3 that's either uncontested or almost uncontested (could be one baddie left in the misogynist pack although not particularly likely). So...the baddies actually aren't too far away from parity. But it's still too far away for a hypothetical Lemeardwulf to try a fake outing I think.