Don't focus too much on getting all 4 substats right. What's more important is you get the right substats upgraded instead. (e.g. 1 atk % substat on a ring hardly matters if you got 3 procs on Def%)

To answer your question, atk stat doesn't affect champs whose skills and damage is based on HP or Def. However like I pointed out earlier, 1 stray substat hardly matters if you have good rolls on the substat you need in the first place.

Thank you for your answer. But, nonetheless, it seems silly to not being able to get ideal items (it hurts me, because I am a perfectionist).

If the abilities from the champ says "Damage based on: [DEF]" it only scales on DEF. (or HP or whatever it  indicates at the description). So yeah, ATK stat doesn't matter at all for those champs.

But mind that not every champ uses damage as utility. At most of the supports abilities you may read "Damage based on ATK" but they scale really low, because their objective is being useful by placing debuffs or whatever, not doing damage, therefor you may be interested in building speed/acc/hp/def rather than attack (even tho their abilities says that). 

I would highly recommend you to follow some content creators on Youtube/Twitch so you can learn about building champs, and you can always join the Raid Shadow Legends Official Discord server where you can share your doubts and discuss with the community.

The answer to the OP question is No.

A hero who damage scales off DEF will have no use for ATK or ATK %.

The Best Ring to improve your damage for a hero who damage scale off DEF would be:

Main Stat: 

- Flat DEF

Secondary Stats: 

- DEF %

- HP %

- Flat HP 

- 4th stat will be useless ATK % or Flat ATK

You would want the Ring to roll in DEF % for substats.

In the above situation, The ATK % & Flat ATK are useless.

However, I do want to mention something very important. 

The ATK % & Flat ATK can be useful for other types of heroes.

I will give you an example. 

_________________________________________________________

Sometimes, Players like using Damage Dealing champions which scale from ATK in Dungeon.

The problem is they can be very hard to keep alive.

Attack Champions can be squishy.

Sometimes, Players like to use the Accessories to help keep the hero alive.

They may decide to pick the following Ring:

Main Stat: 

- Flat HP

Secondary Stat:

- ATK %

- DEF %

- Flat DEF

- HP %

In this situation, All the stats are helping the hero.

The Champion deals damage based on ATK.

The ATK % help increase the hero damage.

The Champion is squishy so you try to add more survivability.

The Flat HP Main Stat + HP % + Flat DEF + DEF % can help keep the hero alive to survive.

What champion might use a set up like this?

A hero who does damage based on ATK who might be wearing Lifesteal gear.

You go into dungeon with your ATK hero.

The Boss hits you - You survive the hit.

Than you attack the Boss back regaining all your lost health with Lifesteal gear. 

Let me give you one more example:

_________________________________________________________________

Sometimes, Players like using Damage Dealing champions which scale from ATK in Arena.

The goal for this hero is to be pure damage.

Sometimes, Players make Speedy teams in Arena which try to kill enemy in 1 turn.

This hero we are talking about is for all out ATK damage.

Main Stat: 

- Flat ATK

Secondary Stat:

- ATK %

- 2th stat will be useless

- 3th stat will be useless 

- 4th stat will be useless 

Notice, The difference between this example vs. other examples?

Think about it - This champion only mission in life is to go first.

This Champion will go first + kill enemy team.

Why do you need DEF?

Why do you need HP?

The only time you need DEF or HP is when your hero is getting hit by an enemy.

We are trying to create a situation where we never get hit by an enemy.

We are going aggressive + fast.

Now you can have a small insight on the different situations which can happen in the game.

I think showing you a few different examples can help you better understand.

Each Ring can be helpful or non-helpful for different heroes.

Example 1 = 1 useless stat

Example 2 = 0 useless stat

Example 3 = 3 useless stat

It all changes depending on what you are trying to accomplish with the hero.

This is a brilliant answer, thank you comrade.