No. Reread the feat, especially its interaction with TWFing. Offhand penalties are lessened, but they are still there. With both, you'll still suffer a -2 on mainhand and offhand attacks. With one or the other, the penalties will be worse. With neither, the penalties will be so great that you'd best forget you even read the rules on them.
EDIT for reference
Ambidexterity [General]
Prerequisite: Dex 15+.
Benefit: The character ignores all penalties for using an off hand. The character is neither left-handed nor right-handed.
Normal: Without this feat, a character who uses his or her off hand suffers a -4 penalty to attack rolls, ability checks, and skill checks. For example, a right-handed character wielding a weapon with her left hand suffers a -4 penalty to attack rolls with that weapon.
Special: This feat helps offset the penalty for fighting with two weapons
Two-Weapon Fighting [General]
Benefit: The character's penalties for fighting with two weapons are reduced by 2.
Two Weapon Fighting
If a normal character (i.e. a character without the multiattack and/or multidexterity feats) wields a second weapon (fights two handed), that character can get one extra attack per round with that weapon. Fighting in this way is very hard, however, and the character suffers a -6 penalty for regular attacks with the first hand and a -10 penalty to the attack with a other hand.
A character can reduce these stiff penalties in three ways:
- If a character's second weapon is light, the penalties are reduced by 2 each.
- The Ambidexterity feat reduces the penalty against the second weapon by 4.
- The Two-Weapon Fighting feat reduces both penalties by 2.
From the 3.0 SRD.
So, if the character has neither feat, and is not wielding a light offhand weapon, they get -6 on main hand and -10 on offhand.
If the character has Ambidextarity, and the offhand is not light, they get -6 on main hand and -6 on offhand.
If the character has Ambidextarity, and the offhand IS light, they get -4 on main hand and -4 on offhand.
If the character has Ambidextarity, TWFing, and the offhand is light, they get -2 on the main hand and -2 on the offhand. Best case scenario.
EDIT EDIT: Its worth noting that the 3.5 ruleset eliminated Ambidextarity as a rediculously cruel and unusual feat tax. Its benefits are now rolled into the TWFing feat.