My wife is literally making me leave the house because I am stressing out so bad over this
. I can confirm though that you do get 3% towards the TLW challenge for match completions, but ONLY for wins. So in theory you can indeed have it unequipped the whole time and just equip it at the very end and that works, but the % hits RIGHT when the match ends so you need to be in-game and make sure you're not gonna die.
After 3 hours and going positive (some games way positive) all but 2 or 3 games I'm at 39%. This quest is horseshit lol. I guess when I get back I'm just gonna play a shitload of Crucible and hope I get paired with randoms that aren't shit so we can win matches. That's 21 wins I'll need, ffs. At least I just got my first purple armor engram from this, and xp seems to be pretty decent in Crucible from kills, so it's not a wash.