For Non-weapon Combat Arts conversion happens iff there is partial physical damage. Some spells do straight ice (FF), while other spells do partial (IS). Although the bar shows otherwise, the conversion only occurs with the physical damage. Thus, converting IS to ice only converts x% of the physical to ice. In general, these conversions aren't enough to really notice. 35% conversion of a spell that has say 40% physical damage is roughly 14% of the damage.
I read somewhere that it should convert all non-specific elemental damage. For example, a weapon that does partial poison (magic, ice, fire) will have all of its elemental converted. Well, typically... Most weapons have elemental damage but aren't 'flaming sword of billybob' specific. So, similarly generic Combat Arts should do the same. I can't think of any off hand. That isn't to say there aren't any.