Silmatenous power supply to arduino nano for an LED dim project

I have an arduino nano and i want to control with it a led strip.
The specs of the project is that i want to control the LED strip with a pot that dims the LED strip, also with the flip of a switch i want to able to control the dimming of the LED strip form my PC. The LED strip, when the control of the LED strip is done from pot (standalone operation), will be powered from the 9V battery that powers the arduino nano.

So far so good i have partly implemented the circuit, i have not implemented the LED output control circuit but the nano sends and dims an LED i have at a digital output. Also the circuit controls the LED when at pc connection when i flip the switch.

My question now. When i connect the arduino nano, or any arduino, at the pc can i have the power connected and ON at the nano at the same time or do i have to power down the arduino?