Freddie went to the Royal Opera House in London in 1981 to see Luciano Pavarotti sing Verdi's "Un ballo in maschera" but he was even more impressed by mezzosoprano Montserrat Caballé and said that he had now heard the best voice in the world. He told his manager, Jim Beach, that he wanted to record with her, and a meeting was arranged in 1987. Freddie recorded a demo "Exercises in Free Love" (the first example in the question) imitating Caballé's voice, and took it to the meeting. She immediately asked if she could sing the song at her next gala, and they started work on what was to become their album "Barcelona". The title song was written for and featured at the 1992 Olympic Games in Barcelona.
So the answer to the question is no. That's really Freddie Mercury singing falsetto in the first example ("Exercises in Free Love", released as the B-side of "The Great Pretender"), but he didn't sing the soprano parts on "Barcelona" as the album was recorded and originally released. Note: there was at least one CD re-release of "Barcelona" which included "Exercises in Free Love" as a bonus track.
There's another audio recording of Freddie singing falsetto at a rehearsal session with Caballé in 1987 together with Freddie's musical director Mike Moran on piano:
On the final recording he wisely left the soprano parts to Caballé.