Yes, you can put in some of your sparge water for the mash out. Mash out is raising the temperature high enough that the conversion enzymes stop working.
Remember one unassailable statistic, as explained by the late, great George Carlin: "Just think of how stupid the average person is, and then realize half of them are even stupider!"
"I would like to die on Mars, just not on impact." Elon Musk