hi i would like to know if i can power the arduino nano with 4 ,1.2v aaa rechargable batteries ?
looks like you can, as long as power is fed into the +5V pin and not the Vin pin (which passes through a voltage regulator first, you don't want that)
The FTDI USB chip won't be turned on unless you hook it up to a USB device, but then again that's probably fine 
I'd imagine if you did hook it up via USB the 5V reference (from the USB port) might try to charge the batteries a little?