Okay, I got the results. I'll provide screenshots if anyone doesn't believe me for some reason. Lol
I went to Elderwraiths and used Ice Strike and Element Composition. Results:
Ice Strike: Did, indeed, do 1 damage, proving they are Ice-immune
Element Composition: Did reduced damage, as if to an Ice-strong monster
Summary: No, any type of immunity does not render the attack harmless. If a skill truly does have two elements, both won't be blocked out by a single immunity.
I went to Elderwraiths and used Ice Strike and Element Composition. Results:
Ice Strike: Did, indeed, do 1 damage, proving they are Ice-immune
Element Composition: Did reduced damage, as if to an Ice-strong monster
Summary: No, any type of immunity does not render the attack harmless. If a skill truly does have two elements, both won't be blocked out by a single immunity.

