From what I understand, prisoners in concentration camps often were tasked with producing supplies for the German military during the war. Were they an essential asset for Germany's production during the war, or were they more of a minor bonus?
This is a more complicated question than it seems. Mostly because the camp and forced labor system of the Nazis was so massive and so varied. Three different examples:
You have the 'work' done at the main concentration camps. One example is Monowitz (or Auschwitz III--not to be confused with Auschwitz-Birkenau, the adjacent death camp), which was associated with the Buna camp (run by I.G. Farben, I believe?) which was supposed to make synthetic rubber. Despite resources being directed there--and despite slave laborers being worked hard (in many cases worked to death) it never produced any synthetic rubber. Similarly, the giant quarry at Mauthausen (the concentration camp in Austria), produced some stone: it was run by the SS Earth and Stone Co. I don't know how much stone they actually worked out of the quarry, but the death toll with the slave laborers (and the infamous "stairs of death" the half-starved people hauled 100 pound stones up) was very high.
On the other hand, many camps 'hired out' slave laborers to German businesses. (who often paid the SS for the 'work') So you have munitions factories, etc., having very low-cost workers forced to make armaments: these smaller-scale camps, connected to businesses, I think were very productive. (the German rocket program used 1,000s of slave laborers in production of V2 Rockets.)
But then there's the whole question of expropriated and stolen wealth. HUGE quantities of gold, silver, stocks, bonds, land, currency, etc. were taken from Jews throughout Europe as part of the machinery meant to extract or extort wealth from them. This could range from extorted wealth from German Jews fleeing (and buying their way out) in 1938, to the gold fillings pulled out of corpses in the crematorium of Auschwitz. (which murdered 2 million people)
Gotz Aly (Hitler's Beneficiaries) argues (with much evidence) that 5% of the German war expenditures were funded by stolen or expropriated wealth from Jews. Other historians think this number is probably too high... but it was a great deal, for sure.