The answer to this depends on how predisposed you are to sing through your natural experiences and abilities. Almost anyone can learn to sing basic tuned songs, but actually singing, at the highest level your potential allows, is going to take a lot of hard work. Research carried out by several universities has shown that training and practice are more a factor than the natural ability to learn to sing. This means that, wherever you are on the talent spectrum, raising your level will require hard work, and by definition, hard work is hard.
Of course, this doesn't mean you shouldn't go ahead. It is a great satisfaction to work towards and achieve a difficult goal. Start with the basics and then gradually move towards more challenging goals with your singing. Yes, anyone who can speak can also learn to sing.
However, the sound quality of the voice depends on several factors. Regardless of a physical vocal disability, with the right training, anyone can learn to sing properly to sing most basic songs. Anyone can learn to sing, it's a skill, not just a talent.