In Fallout 4, Gun Nut returns as a feature to enhance projectile weapon modifications, and it also enables the player character to build heavy turrets in their settlements.
The missile launcher is actually a Big Gun, and so it will not get a bonus from this perk but instead would benefit from the Size Matters perk.
Each of the three ranks of this perk permanently increases the player character's Repair and Small Guns skills by five points.