Body as a power supply
No, we are not a walking battery and we don't generate the voltage seen when we touch probes - that voltage is due to capacitance between our bodies and the wiring in our homes/labs and ground.

The only current our bodies generate is to control muscle activity. This is measured as a signal by ECG machines and measuring that signal produces almost virtually useless amounts of power - enough to be amplified and displayed but not enough for any practical purposes.