Yep. As Duskweaver said, officially the aquila is red and the shoulder trim shows the company color. Some of my old models as examples:
Captain Eshara of 3rd company:
Captain Taelos of 4th company:
My very old 10th company command squad:
10th company has no company color, so the trim is just the usual armor color. In the case of Imperial Fists that makes the Captain of 10th company easy to confuse with the Captain of 2nd company, which has yellow as its color.
As a way to distinguish your Captain each company also has a geometric design associated with it combining the standard armor color and company color. For 2nd company this is a vertical yellow bar down the middle of a chapter color field. 3rd company has a red, diagonal bar (bottom left to top right) instead. 4th company has a green top half.. 5th company is quartered, with black in the top left and bottom right. These designs are meant to go on back banners and the right shoulder pad in place of or in addition to the unit marking usually found there. If you have neither a back banner nor room on the shoulder pad, one of those little heraldic shields that go on the shoulder pad or one knee pad are a good place to put these markings instead.
To the best of my knowledge black has only been popularized for Imperial Fists after the Horus Heresy series took of, outside of 5th company markings. It is not a traditional color and the only Imperial Fists to wear Black in any noteworthy amount were the first Emperor's Champion, Sigismund, who went off to become the basis for the Black Templars color scheme, and of course Chaplains. In any other case black is only notable as part of the chapter badge.