Yes, because there are always bigger guns
If this is a tool using species, as they would have to be to construct augmenting armor, then they are also making new ways to kill each other.
The evolution of warfare is pretty clear on the subject. Weapons will evolve to counter the increased effectiveness of armor. Always. Armor will evolve to counter increasingly effective weapons. Always. Evolution of this kind progresses until some plateau is reached where the cost of armor or weaponry exceeds its benefits.
Armor doesn't have to just stop incoming damage. It can be a means to dealing damage too. A restricted view of armor could be "Things you strap on to make combat hurt less". But, more broadly, armor can be "Things that make combat hurt less but also increase mobility and lethality." Under this broader interpretation, a tank is additional armor that increases survivability, mobility and lethality.
Military power is the ability to project power at a distance. This started with melee range weapons, the reach of an arm. Longer "arms" in the form of ranged weapons came next. Armor to defeat melee and ranged weapons started almost as soon in the form of shields or strap on armor. The entirety of human weapons and armor can be wrapped up in the drive to to extend the range and lethality of weapons and simultaneously increase the ability to resist damage of armor. I see no reason why your creatures with super armor would be any different.
The bigger gun
Eventually, someone is going to invent a weapon that defeats the natural armor so well that the natural armor doesn't even matter. That will force the adaptation and utilization of additional armor to counter the new threat.