If I got a mage through Helgen on legendary, you could certainly get an archer out of there
As for Bullseye, it's paralysis chance is 15%. Bringing the skill to 100 in order to get it, may not be that hard, if you really focus on the skill. However, what you describe, doesn't cover what happens when Bullseye fails -because it will. This, is because in order to get to Bullseye, you had taken Quickshot and before that, Powershot: 50% stagger chance.
Stagger, is the real workhorse in Skyrim's physical weapons combat, whether it occurs from bashing, power attack, or a perk -magic combat is different, since there's an array of methods of avoiding getting hit.
Even when everything else has failed you, stagger will not. So, either you know how to bash, or switch to panic mode and start running like a... ah well, I wrote it too many times arleady