Is it possible to gather data while the Arduino is being powered with a battery, connect to comp, and then read off the values in Serial Monitor?
Yes, this is perfectly possible. You will need to write a routine that you can trigger via Serial. For example you will listen on Serial until you get the dump command. Then run a function that spits your variables out to Serial.
You just have to be careful where you save your 5 variables.
If stored in memory (RAM), you should avoid power loss. Therefore I'd suggest a FTDI USB-to-Serial adapter. There you just connect the TX, RX and GND wires and proceed with the Arduino IDE's Serial Monitor.
If stored in EEPROM, you can use the regular USB connector of Arduino.