Does finesse do any effect if my luck level is 10?

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).
 
Yes, it will give you an extra 5% chance to score a critical hit. Having it and 10 luck is pretty good if you are playing a character that goes for criticals.
 
get boone as a companion, make sure you get his 1st recon beret, raise ur luck to 10, get finesse as a perk, i bet u get 25% or better for crit chance
 
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