Yeah, sure, but there is no breaking point in reaction as you describe.
Sure a high temperature or high concentration increaes reactivity, but its not need per se. A bleaching agent in its active form (e.g H2O2) is active independent of temperature or concentration.
Temperature impacts reaction speed, concentration in ratio to soil how effective it cleans. Sadly, cleaning in these terms includes our beloved enzymes as well.
In detergents, higher temperatures are used to release the bleaching agents from their molecules or to shift the enzyme/bleach balance towards the bleaching side of things. Or to simply speed up things.