Yes
You don't select the Uno as the board; you select the Uno's port (I will edit my post to make it clearer). The reset mechanisms for boards with native USB (e.g. the ProMicro) and those with a TTL-to-USB converter (e.g. Uno) differ. The Uno will react on activation of the DTR signal and the ProMicro will react on the software reset invoked by opening and closing the serial port at 1200 baud.
THE IDE looks or the bootloader and when you double reset the ProMicro, the ProMicro's bootloader is invoked. If you enable verbose output during upload under file -> preferences, you will see something like the below if you have a valid COM port.
Sketch uses 3460 bytes (12%) of program storage space. Maximum is 28672 bytes.
Global variables use 149 bytes (5%) of dynamic memory, leaving 2411 bytes for local variables. Maximum is 2560 bytes.
Forcing reset using 1200bps open/close on port COM23
You can see that a reset is forced. That is followed by the below where the IDE tries to find a bootloader after the reset attempt.
PORTS {COM1, COM5, COM23, } / {COM1, COM5, } => {}
PORTS {COM1, COM5, } / {COM1, COM5, } => {}
PORTS {COM1, COM5, } / {COM1, COM5, } => {}
PORTS {COM1, COM5, } / {COM1, COM5, } => {}
PORTS {COM1, COM5, } / {COM1, COM5, } => {}
PORTS {COM1, COM5, } / {COM1, COM5, COM24, } => {COM24, }
Found upload port: COM24
COM23 is the ProMicro (normal use), COM24 is the ProMicro's bootloader. In the first line COM23 is still visible, in the next lines it has disappeared due to the reset. Eventually it notices COM24 ({COM1, COM5, COM24, }) and finds the bootloader ( => {COM24, }).
If I would have selected COM5 (a SparkFun RedBoard), the proMicro will not react on the reset but double tapping the reset on the ProMicro will invoke the ProMicro's bootloader and you will get COM24.
