Looking at this trait:

THAT CAN RETURN TO ITS ORIGINAL SIZE: When an adjacent friendly character attacks an opposing character, the attacker may modify its attack -1. If they do and hit, instead of normal damage, replace Pym Pocket Tank with WK MP17-006a Pym Particle Tank on its orange starting line with one of its squares adjacent to the target. If the attacking character is named Ant-Man, Giant-Man or Hank Pym, use the yellow starting line instead. When replacing this character, you may ignore characters and blocking terrain when placing it, then destroy any in squares it’s placed into. Any characters in squares it would be placed into are placed adjacent to it. After actions resolve, any characters placed in this way are dealt 2 damage.

If a character were to use mind control or incap or some other power that says "Give this character a close or ranged combat action (minimum range value 4) that deals no damage." Could they have both the effect from the tank and the power resolve?

I would say no. As the attack doesn't deal any damage there is no "...instead of normal damage..."

In this case couldn't it be argued that normal damage is no damage and that the tank would do it's thing instead of no damage?

Yes, you could argue it, but you shouldn't.

If you do not deal normal damage, there is no ability to "instead of" normal damage.

Per the E and C, no, you cannot make that argument. (So you already have the right answer from others, I'm just notating official rules)

"NORMAL DAMAGE
[C]Damage dealt from an attack using the attacker's calculated damage value (including locked values) is called normal damage."

Mind Control is an attack that deals no damage, which means it does not deal normal damage.

The easiest way to be wrong is to say "I would argue..." or a variant of it. Rarely do I see someone use it and be correct.

I would argue that your statement is dead on.