Nope, not Exalted Weapon Upgrade Stone which is used to upgrade your weapon from quest lvl. I mean Exalted Spirit Stone which can be used to AUGMENT that weapon as description of that weapon lvl 2 says
" PvE Damage +10%, Max HP +15%, Atk. Spd. +15%, Critical Damage for standard attacks +5%, Critical Rate for standard attacks +100. Cannot be enchanted, crystallized, appearance modified, or imbued with attributes. Can be augmented with Exalted Spirit Stone, also Special Soul Crystal can be used."