I think the answer to this question is yes.

Anyone can learn to sing.

But I don't think anyone can learn to sing in any manner whatsoever. For example, I could train and practice the next 5 years and I will never sound like Van Morrison or John Gorka, I just don't have it in me. Everyone has their own individual voice (or in some individual cases several voices), that they have to discover and cultivate through experimentation. I think the main barrier to fully developing ones own voice is the fear of just "letting it all hang out" until the best that you can do finds its way to the surface.

If you are not sure what your own voice is, one of the things I recommend is to listen to different kinds of singers and try to imitate the way they sound on record. The goal of this excercise is not to mimic for its own sake, but to exploring the limits and qualities of what your own voice can do. You will quickly find certain vocal styles that you pick up easily, and others that you just can't get. Also, you will find the mimicry will only go so far, and that in the end your own voice will come through in the end.

And don't be afraid to really let loose in this effort. (I recommend to you the documentary film Say Amen Somebody, where a person instructing gospel singers in a workshop told one of her pupils to stop smiling and start snarling when they sang. "You can't sing with a pretty mouth!", was the way she put it.).

Another suggestion I have is exactly the opposite of the one above. Try as much as possible to sing using your own natural diction. That is, try to sing words the way YOU would typically pronounce them them in normal conversation. No vibrato, no operatic tone or timbre. Just try to talk the words to the melody. You will be suprised at first how much concentration this takes. In all the effort to make the melody or the emotion come out, we stop making words in way that is natural to us, and doing so we lose our own natural voice.

Some individuals who are wonderful at singing in their own voice are Doc Watson, Merle Travis, Mississippi John Hurt. I also recommend the singing of Ginny Hawker, a mountain ballad singer from West Virginia.