Assuming the schematic that @bateske posted above:
No danger to the PC or Pro Micro, but possibly to the battery. (I use the term battery to describe your 4 AAA cells).
As long as the battery voltage remains above the USB voltage minus the D10 diode drop, you will still be running off the battery when plugged into USB. If the diode is a regular type, the drop will be about 0.7V. If the diode is a Schottky type, the drop will be about 0.3V. Assuming a USB voltage of 5V, this means a battery voltage above 4.3V for a regular diode and 4.7V for Schottky.
If the battery voltage falls below the above 4.7V or 4.3V the USB voltage will feed current into the battery. For a non-rechargable battery, this isn’t good (since you should never try to recharge a non-rechargable battery). For a rechargeable battery, this also isn’t good since there’s nothing to limit the charge current (other than the F2 fuse or a fuse in the PC), so you could end up overheating or otherwise damaging the battery.
I would put a Schottky diode in series, between the battery + and RAW input, to protect the battery.
If you want to actually power the circuit from USB, I’d consider also adding a switch to allow you to disconnect the battery.