You don't really meet that many armored foes that early in the game, so it's a questionable advantage. Besides, Lucky has a whopping 12 points of damage per hit more than That Gun, and 5.56 AP ammo reduces DT by 15; that gives you a difference of what, 3 damage points? Not much. If you have the Cowboy perk, That Gun gains 4.5 points while Lucky gains 7.5 points, giving it an equal damage-vs-DT output to That Gun WITH AP ammo; add .357 JFP handloads which lower DT by 3 and Lucky is hands down superior.
i don't take the cowboy perk, and in addition, the reloading time of lucky is atrocious, that is a big thing to me especially due to the small mag size.
still, i use lucky quite extensively, it's my early to mid game main weapon combo together with ratslayer, and is also used as my casino gun.