When it says that the object does not count against your item total, can you use a resource with it?

No. You are allowed up to three objects, and what that tells you is this object doesn't count against that total. But it's still an object on your force, and as such is prohibited if a resource is run. For wording that allows a special object and a resource look at CA Captain America #40:
"THE SHIELD (LIGHT OBJECT): The Shield can't be destroyed, only #CA040 Captain America can hold or pick up The Shield. When used in a ranged attack, Captain America may target two characters and deals 3 damage to each hit character. After any attack using The Shield involves, place it in a square adjacent to a target's square. This object does not count toward your force."

I think it just refers to the three objects you are allowed to play when building/revealing your team. (One Heavy, One Light, One 'Any') So you could still play those three as well as equipping Wonder Girl with the lasso.

But I think resources would still nerd this.

edit: Ninja'd by necrodog

Setup - Infinity Gauntlet dial begins on the green line, but does not have a KO click; the dial may rotate past the starting line. You may not add special objects to your force if Infinity Gauntlet is part of it.

Doh, it was worth a shot. Thanks for the answers.