I say sure.
MY own stories, not only is the captain not a human, but neither is about 90-95 percent of the crew.
Check it out:
*bridge and uniforms might change, depending on the era I choose to go with.
As you can see:
Vulcan captain, A Dalek first officer, an Andorian navigator, helm is an Orion, the doctor's an older black human, a green haired yeoman, and the red head's an alien I made up. And the rest of the crew's made up of a bunch of other aliens as well. Not exactly a run of the mill crew line up, but I think if the stories are good, and the characters are likeable, it can work just fine.