Yes, at least to some degree. The biggest factor that limits most people who “can’t sing” isn’t actually their voice, it’s their ear. The ability to hear the note clearly in your head(before you sing it) and match the pitch with your voice. This is 100% trainable with time and practice. Some people just have an innate ability to stay perfectly in pitch, but those who don’t can absolutely learn. The other factor is your vocal chords. I have a deep natural baritone singing voice and there’s lots of songs in the mid range where I just can’t comfortably hit the notes even with lots of practice. I either transpose it down an octave and sing bass or up an octave and sing falsetto
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