Navy absolutely is a City colour. We've had navy socks for more of our history (nearly double the amount of time than sky socks which we've only had for about 40 years) than any other colour. 74 years of our entire club history we've had navy socks and that seems to just be forgotten by the club who never get a kit with navy socks anymore.
The most common kit we've had is:
Shirts- sky blue with white trim
Shorts- white
Socks- navy
That colour combination is unique. Zenit, Lazio, Celta Vigo, Coventry... are all sky-white-sky or sky-sky-sky making us stand out from other sky blue clubs.
That doesn't mean it has to be in the badge of course but it is certainly a City colour.