there are two separate major componants involved with "singing" - the brain and body ( combination of vocal chords, mouth/face, hearing parts, breathing parts). there are people who are atonal because the brain connections aren't in place to synthesize the final product we call music. There are some interesting books out there on the subject - interesting for the geeks, anyway.

Assuming that the brain can interpret sound waves as music, then the question is can the body perform all the needed tasks to reproduce sound waves that another person will interpret as music/singing.

I tend to believe that if you can talk and hum, then you can learn to sing... just how well is the question. But if the physical tools are there, a person should be able to improve their singing voices with work & some guidance.