We've probably all played other role-playing games, both paper- and computer-based. And the generally accepted balance for dual-wielding weapons is to basically balance then to have a higher attack rate, but a lower accuracy. This works well in a system like Fallout's combat system, since accuracy is intimately tied to the amount of damage one does. So yeah, you'll hit them more often... but the shots won't hurt as much.
In as much as this is true, making it take more AP to fire each gun would be a bad thing. Really, if you have two of the same gun it would be just as good to make it take LESS AP to fire the weapon, and trading off animations of which gun you're firing each time. With, of course, lower accuracy on each attack, since you can't hold the weapon as steady.
It would also be good if using two weapons automatically removed the "aimed shot" ability, but without giving the Fast Shot bonus automatically.
Two-handed burster builds with Bonus Rate of Fire, Bonus Ranged Damage, and Living Anatomy would become pretty sick... but honestly they should be.
And just in case anyone decides this really IS a good idea, let me be the first to say "ONE HANDED WEAPONS, ONLY!"