Yes, Free Persons of Color were indeed listed in the pre-1840 Census, just as Lisa and Arlene have previously mentioned.
One word of caution though, if you are using Ancestry.com. In some of the the early census they have neglected to include the entire page, in particularly, the right side of the page that has the columns for FCP & Slaves. For whatever reasons, at least in some of the North Carolina pre-1820 census, as a matter of fact, only the first 3 columns appear in their images, they aren't in the pages either before or after; but when looking at the same images on other sites, such as Heritage Quest, one can see that Ancestry didn't film the bottom of the pages which includes the last 2 columns. This is something I've complained to Ancestry about for years, and they still haven't done anything about it, claiming they would have to re-film those pages at some point in the future.
So, if you ever come across such a situation, I would suggest looking at the images from another source as I did.