Is there a way to monitor a sensor’s activity on an Arduino while powering the circuitry with a battery? How can you connect the RS232 connection on the Arduino to monitor print commands? Do these questions make sense?
The questions make sense, but why do you want to do this? You can power the Arduino from a 9V battery and still connect USB to see the sensor values.
However, to answer your question…I’m pretty sure there aren’t any RS232 level signals on the board. Arduino uses the FTDI chip to translate the TTL level serial communication to USB. If you don’t want to use USB, you could access Rx/Tx on the Arduino and connect them to a level shifter, which is connected to a serial cable.