Alternate power source for Nano

I have a AC/DC adapter, rated at 5V, 0.6A , with USB connector. If I plug that into the USB port of a Nano, to use as an convenient substitute for an external battery, will I blow the board and/or destroy the programming?

Should be fine. If you're worried you could measure the voltage with a multimeter to make sure it's actually putting out 5 V before connecting it to the Nano.

Thank you for the clearance. I'm only worried about blowing another piece of equipment that is a "black box" for me.

If the adapter is actually a battery charger, the filtering may be slim to none. Batteries can be charged with DC pulses as well as pure DC.