Not all the way, unfortunately. Bronjahm turned out to be able to take quite a bit of punishment. I popped my trinkets, put up Time Warp and Mirror Image, and commenced to blowing through my mana like there was no tomorrow. 30 seconds later, I had him down to about 30% health when my mirror images disappeared and he decided to start melting my face off.
I was completely ignoring the corrupted soul fragments, though. I suppose that if I paid attention to those, I wouldn't have had quite as difficult a time getting him down. I'm thinking that it might be worth it to (a) lay out some cash for some higher-end consumables, and (b) plop down 40 Tol Barad Commendations for a Baradin Footman's Tags. Depending on how survivable the footman is, a combination of Mirror Image followed by a Footman may give Aeth enough time to overpower Bronjahm.
Good news is that the trash packs were tough, but not so tough as to be overpowering. There are a couple of 5- or 6-mob pulls in FoS that were a bit hairy (as in, "finished off the last mob with 1% health"), but a using trinkets on cooldown and all of Aeth's many CC abilities helped keep those fights manageable. If I keep it up, I may be able to get her her own Battered Hilt.
So, making a complete SWAG, it looks like Aeth should be able to solo normal Wrath dungeons up to the Nexus (modulo any "you need at least two people to beat this boss" mechanics like Svala Sorrowgrave). Next up is trying to gauge heroic difficulty... I'm thinking to give Heroic Drak'Theron a try, and see how that works out. Maybe pick up an achievement on the way!