I was thinking, would this be possible? If one used Enchanting/Alchemy and just got a very powerful damage enchantment on a simple bow, would it be strong enough to strictly rely on?

I just think robes + bow looks amazing, and a magical archer would be a fun type of thing. I wouldn't put too many perks into the Archery tree itself, and I'd have to not use a bound bow cause you can't put damage enchants on it.

But with the fortify restoration potion glitch, would this be viable?

I've never used the fortify restoration glitch so I wouldn't know. Also, if anyone has any ideas to make this build more complex, please post. I've never heard of this idea and it's purely an original one, so I'm gonna need some help constructing the build.

If you do the fortify restoration glitch, you could enchant a ring with fortify archery +100000%. Done.

I'm kinda looking for along the lines of 100-200 damage with just the enchantment, like "Burns the target for 180 Damage", not actual archery damage.

With 100 enchant and the dual perk, you can make a 150ish magic damage weapon. (also requires 60 destruction for the augment perks) That should be enough. No exploits required.

If you take Archery and Sneak backed up by some judicious Smithing and Enchanting you'll be fine, though you might want some poisons in the early/mid levels. With that build you don't need armour because the only time you'll get hit is when you foul up, but you would need to put some perks into the marksman tree. Without sneak an archer is just a practice dummy for every sword-slinger, axe-maniac and mad-mage in the game.

You should consider using destruction for runes. Setting up some nice traps will add another layer of fun for ya.

The archery skill maxed out along with items enchanted to fortify archery as well as an enchanted Daedric bow will get you the following based on my experience;
Daedric Bow (epic) = 106 damage
Fire enchantment = 56 damage
Arrow = 24 Damage
Circlet of Major Archery = + 25%
Daedric Gauntlets of Archery = +32%
Amulet of Archery = +35%
106+56+24=186*192% = 357 Base Damage not counting Potions for increased fire damage or potions of true shot. I kill dragons with 2-5 arrows depending on the type of dragon.

I am a Mage/Sniper and love it.
Bonjoyle