Retroaction on Arduino from external power supply?

I have a pressure sensor (AMSYS5812) in a device I design for use in student's labs, which has analog and digital (I2C) output. It can use both modes alternatively - analog output for those who want to read pressure values without a computer. They need only a multimeter and an external power supply, which connects to the Vcc pin of the sensor. For those, who want to register the values with an computer, an Arduino nano is built in, which is connected with the I2C lines. The 5+ pin of the Arduino is connected with the same just mentioned Vcc pin of the sensor. In this case no external power supply is needed, the power is supplied by the USB connection. Now it would be possible (no one knows which people will use this), that one uses the external power supply while the USB jack is still connected. Then the 5 volts of the power supply will flow into the +5 V pin of the Arduino. (GND pins of power supply, Arduino and sensor are connected, the external 5 volts come from an 7812 IC). Would that be fatal for the Arduino?

Thanks for answering - Richard

Are you asking whether a nano can be powered both through the USB connection from a computer, and through the 5V power input ?

The answer would seem to be yes, but only if the ground 0V level was the same, or could be forced to be the same. This is not impossible, but introduces various potential complications.

Yes, that's the essence of my question. All ground pins are connected, i.e. they share the same potential. I could use a diode to make sure, that the Arduino is only powered by its USB connector, but I want to avoid this, because a diode causes a voltage drop.