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I waltzed through Shadows of Amn and Throne of Bhaal with an Elven Barbarian my first time through. Take my word that I didn't understand the magic system one bit (I only used offensive spells). I made it just fine, so it's certainly possible.

As Sir Degrader said, some area's in the game can be quite hard, a particular fight in the Planar Sphere for instance, but if you just keep hacking with your weapons and keep gulping down those potions then you'll be just fine, I suppose.