Yes all calypsonians adopt a character or persona. This is a distinguishing feature of calypso in my opinion -- the songs are sung from the POV of the calypsonian in character.

Even in a third-person song such as Invader's "Prince Rainer" he inserts himself into the song, saying they should have invited him: "I am positive they would have been so glad/to hear the Lord Invader from Trinidad".

Compare/contrast with modern popular music which is sung from the POV of the singer as themselves, or folk music (since the '50s revival) which is sung from the POV of the character in the song. That's why Bob Dylan could sing "It's been the ruin of many a poor girl" in "House of the rising sun" but Eric Burdon had to change it to "poor boy".