No, by definition, Race is below Species.
Apis mellifera is the Western Honey Bee species, but it is subdivided into multiple races. What makes them a species is that they can all breed and produce fertile offspring -- each race is identified by distinct, recognizable genetic traits.
Humanity is a species -- all humans can interbreed and produce fertile offspring. Within humanity there are groups that have distinct, recognizable genetic traits.
Arguing semantics and redefining terms is not going to solve the problem of racism and bigotry. Too much time is spent worrying about the specific words people use and not enough addressing the underlying issues. To use a newly popular phrase, putting the lipstick of semantic change on the pig of racism doesn't do a damn thing to fix the problem.
In the last hundred years, the "right" way to describe people of African descent in the United States has gone from Negro, to Colored, to Black, to African-American -- the last three were driven by that community, and none of those changes had a quantifiable impact on racism or bigotry. All that changed was the words.
Concentrating on words is pointless, because the underlying problem, the mind of the racist, doesn't care one little bit about what words are used. Time and effort is spent complaining when a Spanish teacher teaches colors (black=negro) or when someone uses the word niggardly (because it sounds like something offensive), while both overt and covert racism and bigotry remain entirely unaffected by semantic argument.
Saying there's only one race of humans, no matter how many times it's repeated or by whom, has absolutely no impact on someone who judges people by the color of their skin. Saying that there are no differences between human races is actually counter-productive, because the racist can see with his own eyes that there are genetic differences between the groups of people and since that argument is now proven wrong to him, anything else you say must be wrong as well.