i haven’t under this particular one but have come across other guys working on temporary visas.
its difficult to give more info without knowing which country you would need it for, but the documents you need to provide are largely the same.
In Ireland the process was very easy - booked appointment online, showed documents and got a passport stamp so my wife had proof of her rights until official permit issued (approx 7/8 months).
In Italy it was a total mess. No appointments just go to the local immigration centre, fight your way through the crowd at the front door when it opens and stand in line for hours hoping that you’re far enough forward in the queue to get seen that day. Took us three goes to get it done, and no temporary stamp which caused us a few issues as even though my wife was entitled to be regarded as an eu citizen from day of entry it’s difficult to get people to accept it without the residence permit. Received 5 year doc a bit faster, approx 3/4 months.
its hard to say if airlines would be aware of this so would accept that as sufficient at application stage, but if it doesn’t come up until interview you might have a better chance of explaining it then.