Let’s say you are dying of starvation. You pull one of your teeth out, causing blood to slowly seep into your mouth, which you swallow. The calories from the blood getting digested will delay the time you die of starvation, right? Or will losing blood while starving kill you faster?
That would be akin to running a hose out of your car’s gas tank and back in. You’d use some gas for the pumping and add none back in the process.