My characters intent is to not be overpowered, just an average human who came to skyrim in seek of adventure/treasure and exploration. That means no smithing/enchanting/sneaking. Just training in one hand combat, light armor, lock picking, speechcraft.
Is archery overpowered by itsself? I hear its overpowered with stealth but since I am not using stealth is archery still OP?
I like the RP idea, OP!
And no, I don't think Archery is overpowered, even when in Sneak. By comparison, With the two main Sneak attack Perks activated a sword or dagger can do 6x damage on a successful Sneak attack. A Bow can only do 3x damage. Yes, when Smithing is taken into account, a bow will have any where from 6-12 more base points of damage per attack, but when you figure in the Sneak Attack multipliers a Sword or Dagger will easily surpass the Bow in damage.
And I won't even get into the Dagger specific Perk 'Assassin's Blade'. 15x damage is just sick, and if you get the Dark Brotherhood armor (the gloves specifically), then all of your Sneak Attack damage with One-Handed weapons is doubled... that means Swords, Axes, Maces, etc. hit for 12x damage, and Daggers do an insane 30x damage! Meanwhile, a bow is stuck at 3x damage for a Sneak attack.
So no, I don't believe that Archery is overpowered. I think that even if you pump everything into Archery, you will do no worse (but certainly no better) than you could do with a Sword or Dagger.
I have played in Assassins' Guild with every character I have ever created since Morrowind, I just love the Morag Tong and the Dark Brotherhood so much! They're absolutely my favorite character type, and the above paragraphs are just a couple of reasons why.

Hope this all helped.