Absolutely not; because at the end of the day, the Soviet Army Groups that fought in the Battle of Stalingrad never lost their ability to fight. Body counts and material losses, to put it bluntly, are important; but only to a certain extent. Efficacy and ability to fight on are the most important part of full spectrum combat; is the enemy a cohesive force, is his will to fight unbroken, is his physical ability to fight unbroken, can/will the enemy fight if pursued?

For the German 6th Army, all of these questions end in a resounding 'no.' The army as the Germans know it, ceased to exist; and it was a blow from which the Germans never truly recovered. Their ability to continue to wage combat at the same intensity before the battle never recovered. For the battered 62 Army, and the Don Front it was apart of, it was back in action within a matter of months. It was yet another degrading of their combat ability from 1941 (A broad, 3 Army Group wide offensive); combat operations in 1943 would stretch the Wehrmacht to the limit to retain the same offensive power of the combat operations in 1942.

I would refer you to this question where myself and /u/elos_ go into more depth as to why the 6th Army was defeated, and why it should be considered a decisive, not Pyrrhic, Soviet victory.

TL DR: For the Soviets to have 'won' a Pyrrhic victory, their ability to continue their tempo of operations would have had to have been drastically reducted. It was not, rather, it completely shifted the initiative in their favor and allowed them to step up their tempo of operations. The exact opposite of the definition of a Pyrrhic.

The Battle for Stalingrad, my bad.

A pyrrhic victory has to fullfill some criterias, first and foremost you have to be worse off than you were before in relation to your enemy.

The eastern front was a prime example of a war of attrition and therefore a important part of examining the outcome of a battle are the casualties and equipment losses. Comparing the casualties alone is not enough because the Wehrmacht and Red Army had different ressource situations. The Red Army was able to draft more people and could outproduce the Wehrmacht ( eastern front units ) this means the Red Army didn't need to inflict the same amount of damage to the Wehrmacht to leave the battlefield with a favorable outcome. Furthermore Germany was on the clock so to speak, so even holding of the Wehrmacht and staying in the war was a little "victory".

In another comment it is mentioned that the Wehrmacht didn't recover from the loss of the 6th Army. This is incorrect and not really important. What does "recovering" mean in this context? The Wehrmacht peaked in 1943/44 but had to divert ressources to other theaters. The German armies around Kursk 43 were certainly more powerful than the German forces in 42 but had to face off a significantly stronger enemy than in Operation Blau. Here you see the attrition is an important factor. The side which can bring more men and tanks to the front will win unless the other belligerent is able to inflict so much casualties that hes able to compensate.

Was Stalingrad a Pyrrhic victory?

No. For the Red Army this was one of the most favorable outcomes in terms of casualty ratio ( for the early war ). The loss of life on the Soviet side was without a doubt unneccessary. The German attemps to reliefe Stalingrad were stoped and the fast advance into the southern Ukraine was eventually a failure ( 3rd Kharkov battle). There was no real hurry to reduce the Stalingrad pocket. Nevertheless the outcome was favorable for the Red Army.

Nevertheless there is certainly a mystification of the battle. Stalingrad gets made more significant than it really was. While it was a turning point for the public eye it was just another battle after the real and only turning point in 1941, which showed that the Wehrmacht was incapable of inflicting enough damage to collapse the Red Army before getting outproduced/drafted.