As noted, you can't do the Arena that way - Owyn won't let you fight unless you're in the Arena armor.
There is a mod that adds a ring to the game which substitutes for the arena armor, allowing one to wear whatever one wants. I believe it has an unenchanted option, so it would be the equivalent of just wearing the prison clothes.
He made it to about, IIRC, level 5, then hit a wall. The world just started getting too dangerous for him to keep up with it armed with nothing but his fists and in nothing but a pair of shabby pants.
Yeah, you can't use poisons, and you have almost no ranged attack at all (the OP's suggested flare spell is too weak to be useful very long, and it's basically useless against all the dunmer archer bandits in the game.) The only way I can see that this would work is to prevent leveling almost completely, to keep that spell and the starting healing spell useful; you'd have to either never sleep, or set the character with all never-use majors.
I've played a character similar to this, but with the further "rule" that my character was able to use anything freely given to her. So, once we got a short way into the Main Quest, she had acquired a nice lightly-enchanted cuirass, from her friend in Kvatch, and a very good katana with her induction into the Blades. She was a Breton, though; I also have my doubts about any elf being dumb enough to try this.
A Nord, now... A Nord might even throw away the prison suit, or have it stolen by a Witch... Any Morrowind players here...?