it does, and you can check it yourself by looking at the "crit chance" stat in the character sheet: a character with Luck 10 has 10% critical chance, while a Luck 10 + Finesse character has 20%. Of course we are talking about a character without any perk that increases crit chance. But Finesse will effect your stat.
However, I wouldn't recommend taking Finesse because it'll decrease the damage you do to enemies. Take a Luck character and later in game take the perk Sniper (for Small Guns/Big Guns/Energy Weapons) or Berserk (for Unarmed/Melee).