No. It is done in certain southern states in the US and among certain ethnic groups elsewhere. It is quite hazardous to learn pronunciation from singers singing songs.

It's not a question of formality or informality. Many accents do indeed pronounce 'I' as 'ah', in particular those from the Southern states of the US, and also some Scottish accents. And as Michael says, 'ah' is almost universal as a pronunciation in popular music. Why? Because it sounds better with music.

"Ah" is the way "I" is pronounced in many English accents in informal speech e.g. US, Canada, Scotland. "Ah" is almost universal in English pop songs the world over, even from English groups e.g. "I can't get no (satisfaction)" by the Rolling Stones. This reflects American influence. But contrast this with e.g. "I like driving in my car" by Madness, in which the "I" sound is spoken with a London accent and does not sound like "ah" at all.

I would not say that it's common in general, but it is somewhat common in this style of music. This same singer likely would not pronounce it that way when she's speaking.

In the word "I", the vowel sound is a diphthong. It slides from an "AH" sound to a long-e "EE" sound, very quickly: AH-EE. Different regional accents put different strengths and durations on the two vowels. In some Southern dialects it becomes close to a pure AH. It is common for singers to distort English vowels. English has a lot of closed vowels that do not produce a nice, clear, ringing tone. Singing teachers teach singers to extend some vowels and minimize others. People who say "AH-EE" are taught to sing "AHHHHHHHH-ee." Italian has vowel sounds that are good for singing. It was once customary for opera singers to use Italian vowels when singing English. Unfortunately, in English anyway, singers must compromise between clear diction and beautiful sound. You can see the results on any Internet lyrics site. Listening to a song, you are rarely sure what all of the words are.