A 51

This would not work at all. While a character with improved unarmed strike is considered armed, he is not holding any weapons. Even a monk's unarmed Strike (which the unarmed swordsage gets) does not help as his attacks are only considered manufactured/natural weapons for the purpose of spells and effects that enhance manufactured/natural weapons. The Raging Mongoose boost enhances the character, not the weapons. So he gets zero additional attacks.