It definitely would not be nearly as successful and I don't think she has the proper vocals AT ALL for that. It'd be interesting though, if she were to release it at the right time in her career and the song had softer vocals it could do semi-well.
PREVIOUS RESULTS
Britney Spears - "Teenage Dream" (song) - not as successful
Rihanna - Crazy In Love (feat Jay Z) - not as successful
Ke$ha - Super Bass - not as successful
Katy Perry - The Edge of Glory - just as successful
Lady Gaga - Run The World (Girls) - more successful
P!nk - "Stronger (What Doesn't Kill You)" - more successful
Christina Aguilera - "California King Bed" - not as successful
Beyonce - "Criminal" - not as successful
Kelly Clarkson - "Hurt" - more successful
Nicki Minaj - "Fergalicious" - not as successful
Mariah Carey - "Single Ladies (Put a Ring On It)" - not as successful
Madonna - "I'm Every Woman" - not as successful
I think it would've been more successful. It would've been massive on urban radio for starters. Even though Someone Like You as a song is suitable for that format, it didn't get supported there (probably because Adele is white tbh), so I think if Alicia Keys did it, it would've got sky-high radio airplay, and she's had massive hits with similar-ish songs before.