Is the TX-Pin of a Pro Mini an input until...

Is the TX-Pin of a Pro Mini an input until the Serial.begin() statement in the setup?

I want to interface it with the UART2 of a Raspberry Pi on GPIO 1, which is shortly an output upon booting.

All pins are inputs until programmed differently. On Arduinos the bootloader will take control immediately after power on or reset, and uses RX/TX to listen for possible program updates. I don't understand what's different with the RasPi. It doesn't make sense to program a pin for output, that afterwards is used for input.

You know that you have to cross over the RX and TX lines? RX is the input, TX the output of each port.

The current between two outputs can be limited to harmless values by separating them by a resistor (about 1k).

DrDiettrich:
It doesn’t make sense to program a pin for output, that afterwards is used for input.

The GPIO1 on the Pi4 which can carry the UART2 RX functionality is normally not free to use.

It is used by the firmware to identify the used HAT(Shield) over a TWI interface upon bootloading.

After a few milliseconds the (in my case failed) identification is finished and the pin is released.
So it will be output (SCA) just for ~20mS and then can be used for RX.

I have got no control over that.

Be sure to use a 3.3V Pro Mini with RPi.

jremington:
Be sure to use a 3.3V Pro Mini with RPi.

Of course. That is the very reason to chose a Pro Mini!
I have them on a self made HAT, and they are completely programmable from /dev/tty AMA0.
With VNC I can even program them worldwide!