Not without a boosting item, it doesn't. I'll show you.
With
this damage calculator, I got this:
252 Atk Haxorus Outrage vs 252 HP/252 Def Quagsire: 47.97% - 56.6%
2-3 hits to KO (with Leftovers)
Possible HP Damage: 189, 192, 193, 196, 198, 201, 202, 205, 207, 210, 211, 214, 216, 219, 220, 223
With
this damage calculator, I got this:
432 Atk vs 295 Def & 394 HP (120 Base Power): 189 - 223 (47.97% - 56.60%)
Heck, I just ran another calc, and even 0/0 neutral Def nature Quagsire is not OHKOd by Adamant Haxorus's Outrage unless it holds a boosting item.
So if there was ever proof that Quagsire is an absolute boss...there it is.