HOWTO: Airspy mini and Airspy R2: Piaware / dump1090-fa configuration

You’ll have to test that it works anyway.
Having access via putty is also very helpful in such situations to adjust gain for example.

But yes it will start automatically.

In regards to putty, you can follow part B of this how-to:
For Beginners - How-to SSH to RPi - Setup Putty in Windows

You should change the password of the default user (not sure about the default user on your image).
Then you might also need to enable ssh

sudo systemctl enable ssh
sudo systemctl start ssh