In your example, yes, it would be capitalized. If you were referring to the color, navy blue, it would not be capitalized, unless it was the name of the thing you were referring to. Hope this helps.
Normally in the grammatical English, the proper nouns are not capitalized as a whole. Rather their first word is capital even if they appear in the middle of the sentence. For instance Navy, Army, Air Force etc
Actually all the proper noun must start with a capital letters irrespective of where they occur in a sentence there fore the first letter need to be capitalized.
I agree. Navy should be capitalized in this example, the other (navy blue) does not need the capitalization.