(That would make for a fun character btw: unarmored priest dual wielding maces.)

Skyrim provides quite a few ways to do this (armor, spells and actually moving your character out of harms way) so even an unarmored mage could pull off dual wield in theory. There are plenty more builds to think of, but since you are indeed vulnerable to incoming blows you'll need some way to negate or dodge incoming damage. The sneaky character had to hit multiple times though for killing anything above bandits since master difficulty gave enemies extreme amounts of health (or just nerfed your own damage). Both characters were played on master difficulty (I like the challenge), which means you'll have to be very patient (aka dying a lot) early game anyway, but when past level 35-40 it becomes almost too easy. The sneaky character pacified (charmed) the attackers, snuck behind them and stabbed them. Next to that I developed a knack for dodging incoming blows which makes fighting one opponent extremely easy. The paladin could heal himself and the heavy armor negated much of the damage.

Sneaky character with extreme illusion and the 15x sneak damage.

I found dual wield doable (and fun) in a few ways:

Skyrim dual wield mods