Yes it is a big part for being an assassin/thief.
No it's not, if you get 2 daggers and dual wield them, and get the 6x damage multiplier perk from the sneak perk tree you can 1 hit KO almost anything.
But, archery CAN be a big part of stealth, I just wet through a dungeon with no Draugr noticing me and picking them off with the bow

It's your choice, like almost aleverything in the game.