Do Item Spell Procs Benefit from Synergies?

If, for example, I'm using a Windhammer which has a 33% chance to cast level 22 twister on striking would it gain increased damage if I'm playing a druid with points in twister? Would it gain damage from points I have in the synergies for twister such as Tornado and Hurricane?

How about the Firestorm procs from Phoenix?

Thanks for your help, I'm new to the game.|||Yep, points spent in a spell's synergies will affect it when it's procced.|||AFAIK, putting points in twister itself won't increase the damage from Windhammer, as it will always remain level 22. However, as stated above, synergies do work as synergies for the skill, which creates some awesome build-thoughts!|||Thanks guys!