I certainly think he does. 

Indeed, that’s the central tension of Tyrion’s arc in ACOK – we’re rooting for him to succeed against Cersei and Varys and Pycelle and Littlefinger, we cheer when he leads the sally from the Mud Gate to the cheers of “Halfman!” but at the end of the day, Tyrion’s success means that Joffrey stays on the Iron Throne.

And this is a point that GRRM hammers home again and again. Tyrion starts ACOK by proclaiming that he’s going to “do justice,” and he’s absolutely gobsmacked to find out that the smallfolk of King’s Landing hate him. And as much as he likes to blame everything on Joffrey and feel aggrieved, Tyrion’s his Hand of the King and doesn’t do a damn thing when Joffrey starts giving orders to murder innocent civilians or shooting starving people with crossbows. 

I would also argue, btw, that a big chunk of Tyrion’s ASOS arc is his realization of his complicity in this regime and his realization of what the regime is like when you’re no longer the man on top…

Now, it’s an open question whether Tyrion is going to reawaken to humanity as @poorquentyn explores in his ADWD essays, but I personally hope that part of that process is Tyrion realizing that it’s not enough to try to “soften the blow” but that one has to defect from the system of oppression and join Dany’s revolution in order to actually “do justice.”

As for Jaime, I think I’ve made my opinion clear on that point: Jaime’s hated because he stupidly refuses to tell anyone what he did and why. But in my opinion, Jaime should be condemned for not stopping the Mad King the moment Aerys gave the command to burn people alive without trial.