Yes, hearing intervals is important...very important

Train yourself to hear and play all intervals. Pick a note, then from that note play a minor second, Major second, minor 3rd, Major 3rd, Perfect 4th, etc. up to an octave, - essentially you are playing a chromatic scale, with the first note in between the notes of the scale. This helps to fine tune your ear, and saves time when you are working on intonation in your piece. You can use a tuner, but also thoughtfully rely on your ear.