Joining a good choir can do a lot to really build your ear in this respect. Generating a note from within your body does so much more to build your ear than generating a note by hitting a key or plucking a string (wind instruments are kind of a middle ground in this respect).

You may be able to sing to it but since it's assuming the instrument to be in tune (piano) it may be slightly off and still register since it's estimating which note is most correct.